Documentation Verification Report

Basic

šŸ“ Source: Mathlib/CategoryTheory/Monoidal/Braided/Basic.lean

Statistics

MetricCount
DefinitionsBraidedCategory, braiding, curriedBraidingNatIso, ofFaithful, ofFullyFaithful, tensorLeftIsoTensorRight, monoidalFunctorBraided, instComp, instId, toLaxBraided, toMonoidal, LaxBraided, id, instComp, ofNatIso, toLaxMonoidal, LaxBraidedFunctor, forget, fullyFaithfulForget, homMk, instCategory, isoMk, isoOfComponents, laxBraided, of, toFunctor, toLaxMonoidalFunctor, tensorMonoidal, tensorΓ, tensorμ, instBraidedMopFunctor, instBraidedUnmopFunctor, instBraiding, instMonoidalMopFunctor, instMonoidalUnmopFunctor, SymmetricCategory, equivReverseBraiding, ofFaithful, ofFullyFaithful, toBraidedCategory, instBraidedCategoryDiscrete, instBraidedCategoryOpposite, reverseBraiding, symmetricCategoryOfFaithful, symmetricCategoryOfFullyFaithful, termβ_
46
Theoremsbraiding_inv_naturality, braiding_inv_naturality_assoc, braiding_inv_naturality_left, braiding_inv_naturality_left_assoc, braiding_inv_naturality_right, braiding_inv_naturality_right_assoc, braiding_naturality, braiding_naturality_assoc, braiding_naturality_left, braiding_naturality_left_assoc, braiding_naturality_right, braiding_naturality_right_assoc, braiding_tensor_left_hom, braiding_tensor_left_hom_assoc, braiding_tensor_left_inv, braiding_tensor_left_inv_assoc, braiding_tensor_right_hom, braiding_tensor_right_hom_assoc, braiding_tensor_right_inv, braiding_tensor_right_inv_assoc, curriedBraidingNatIso_hom_app_app, curriedBraidingNatIso_inv_app_app, hexagon_forward, hexagon_forward_assoc, hexagon_forward_inv, hexagon_forward_inv_assoc, hexagon_forward_iso, hexagon_reverse, hexagon_reverse_assoc, hexagon_reverse_inv, hexagon_reverse_inv_assoc, hexagon_reverse_iso, tensorLeftIsoTensorRight_hom_app, tensorLeftIsoTensorRight_inv_app, yang_baxter, yang_baxter', yang_baxter_assoc, yang_baxter_iso, braided, ext, ext_iff, toMonoidal_injective, braided, braided_assoc, map_braiding, map_braiding_assoc, comp_hom, comp_hom_assoc, forget_map, forget_obj, homMk_hom_hom, hom_ext, hom_ext_iff, id_hom, isoMk_hom, isoMk_inv, isoOfComponents_hom_hom_app, isoOfComponents_hom_hom_hom_app, isoOfComponents_inv_hom_app, isoOfComponents_inv_hom_hom_app, of_toFunctor, toLaxMonoidalFunctor_toFunctor, associator_monoidal, associator_monoidal_assoc, leftUnitor_monoidal, leftUnitor_monoidal_assoc, rightUnitor_monoidal, rightUnitor_monoidal_assoc, tensor_associativity, tensor_associativity_assoc, tensor_left_unitality, tensor_left_unitality_assoc, tensor_right_unitality, tensor_right_unitality_assoc, tensor_Ī“, tensor_ε, tensor_Ī·, tensor_μ, tensorĪ“_tensorμ, tensorĪ“_tensorμ_assoc, tensorμ_comp_μ_tensorHom_μ_comp_μ, tensorμ_comp_μ_tensorHom_μ_comp_μ_assoc, tensorμ_natural, tensorμ_natural_assoc, tensorμ_natural_left, tensorμ_natural_left_assoc, tensorμ_natural_right, tensorμ_natural_right_assoc, tensorμ_tensorĪ“, tensorμ_tensorĪ“_assoc, mopFunctor_Ī“, mopFunctor_ε, mopFunctor_Ī·, mopFunctor_μ, mop_braiding, mop_hom_braiding, mop_inv_braiding, unmopFunctor_Ī“, unmopFunctor_ε, unmopFunctor_Ī·, unmopFunctor_μ, unmop_braiding, unmop_hom_braiding, unmop_inv_braiding, braiding_swap_eq_inv_braiding, reverseBraiding_eq, symmetry, symmetry_assoc, braiding_inv_tensorUnit_left, braiding_inv_tensorUnit_left_assoc, braiding_inv_tensorUnit_right, braiding_inv_tensorUnit_right_assoc, braiding_leftUnitor, braiding_leftUnitor_assoc, braiding_leftUnitor_aux₁, braiding_leftUnitor_auxā‚‚, braiding_rightUnitor, braiding_rightUnitor_assoc, braiding_rightUnitor_aux₁, braiding_rightUnitor_auxā‚‚, braiding_tensorUnit_left, braiding_tensorUnit_left_assoc, braiding_tensorUnit_right, braiding_tensorUnit_right_assoc, leftUnitor_inv_braiding, leftUnitor_inv_braiding_assoc, op_braiding, op_hom_braiding, op_inv_braiding, rightUnitor_inv_braiding, rightUnitor_inv_braiding_assoc, unop_braiding, unop_hom_braiding, unop_inv_braiding
134
Total180

CategoryTheory

Definitions

NameCategoryTheorems
BraidedCategory šŸ“–CompData
2 mathmath: CartesianMonoidalCategory.instSubsingletonBraidedCategory, CartesianMonoidalCategory.instNonemptyBraidedCategory
LaxBraidedFunctor šŸ“–CompData
29 mathmath: LaxBraidedFunctor.isoMk_inv, CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_map, LaxBraidedFunctor.isoOfComponents_inv_hom_hom_app, CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, LaxBraidedFunctor.comp_hom, LaxBraidedFunctor.isoOfComponents_hom_hom_app, LaxBraidedFunctor.forget_map, CommMon.equivLaxBraidedFunctorPUnit_unitIso, CommMon.equivLaxBraidedFunctorPUnit_functor, LaxBraidedFunctor.isoOfComponents_hom_hom_hom_app, CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_obj, Functor.mapCommMonFunctor_map_app, LaxBraidedFunctor.comp_hom_assoc, Functor.mapCommMonFunctor_obj, LaxBraidedFunctor.isoMk_hom, CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_obj, LaxBraidedFunctor.homMk_hom_hom, LaxBraidedFunctor.forget_obj, CommMon.equivLaxBraidedFunctorPUnit_inverse, LaxBraidedFunctor.isoOfComponents_inv_hom_app, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_one, CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, LaxBraidedFunctor.id_hom, LaxBraidedFunctor.hom_ext_iff, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_mul, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, CommMon.equivLaxBraidedFunctorPUnit_counitIso
SymmetricCategory šŸ“–CompData
1 mathmath: CartesianMonoidalCategory.instSubsingletonSymmetricCategory
instBraidedCategoryDiscrete šŸ“–CompOp
14 mathmath: CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_map, CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CommMon.equivLaxBraidedFunctorPUnit_unitIso, CommMon.equivLaxBraidedFunctorPUnit_functor, CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_obj, CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_obj, CommMon.equivLaxBraidedFunctorPUnit_inverse, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_one, CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_mul, CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, CommMon.equivLaxBraidedFunctorPUnit_counitIso
instBraidedCategoryOpposite šŸ“–CompOp
8 mathmath: op_inv_braiding, op_braiding, op_hom_braiding, unop_braiding, instIsCommMonObjOppositeCommAlgCatXUnopMonObjCommBialgCatFunctorCommBialgCatEquivComonCommAlgCatOfIsCocommCarrier, unop_inv_braiding, unop_hom_braiding, instIsCommMonObjOppositeCommAlgCatOpOfOfIsCocomm
reverseBraiding šŸ“–CompOp
1 mathmath: SymmetricCategory.reverseBraiding_eq
symmetricCategoryOfFaithful šŸ“–CompOp—
symmetricCategoryOfFullyFaithful šŸ“–CompOp—
termβ_ šŸ“–CompOp—

Theorems

NameKindAssumesProvesValidatesDepends On
braiding_inv_tensorUnit_left šŸ“–mathematical—Iso.inv
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
BraidedCategory.braiding
CategoryStruct.comp
Category.toCategoryStruct
Iso.hom
MonoidalCategoryStruct.rightUnitor
MonoidalCategoryStruct.leftUnitor
—Iso.inv_ext
braiding_tensorUnit_left
Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_leftUnitor
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_rightUnitor
Mathlib.Tactic.Monoidal.naturality_id
braiding_inv_tensorUnit_left_assoc šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.inv
BraidedCategory.braiding
Iso.hom
MonoidalCategoryStruct.rightUnitor
MonoidalCategoryStruct.leftUnitor
—Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_inv_tensorUnit_left
braiding_inv_tensorUnit_right šŸ“–mathematical—Iso.inv
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
BraidedCategory.braiding
CategoryStruct.comp
Category.toCategoryStruct
Iso.hom
MonoidalCategoryStruct.leftUnitor
MonoidalCategoryStruct.rightUnitor
—Iso.inv_ext
braiding_tensorUnit_right
Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_rightUnitor
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_leftUnitor
Mathlib.Tactic.Monoidal.naturality_id
braiding_inv_tensorUnit_right_assoc šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.inv
BraidedCategory.braiding
Iso.hom
MonoidalCategoryStruct.leftUnitor
MonoidalCategoryStruct.rightUnitor
—Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_inv_tensorUnit_right
braiding_leftUnitor šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.leftUnitor
MonoidalCategoryStruct.rightUnitor
—MonoidalCategory.whiskerRight_iff
MonoidalCategory.comp_whiskerRight
braiding_leftUnitor_auxā‚‚
braiding_leftUnitor_assoc šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.leftUnitor
MonoidalCategoryStruct.rightUnitor
—Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_leftUnitor
braiding_leftUnitor_aux₁ šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.hom
MonoidalCategoryStruct.associator
MonoidalCategoryStruct.whiskerLeft
Iso.inv
BraidedCategory.braiding
MonoidalCategoryStruct.whiskerRight
MonoidalCategoryStruct.leftUnitor
—Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_whiskerLeft
Mathlib.Tactic.Monoidal.eval_of
Mathlib.Tactic.Monoidal.evalWhiskerLeft_id
Mathlib.Tactic.Monoidal.evalComp_cons
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.evalComp_nil_cons
Mathlib.Tactic.Monoidal.eval_whiskerRight
Mathlib.Tactic.Monoidal.evalWhiskerRight_nil
Mathlib.Tactic.BicategoryLike.mk_eq_of_cons
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_associator
Mathlib.Tactic.Monoidal.naturality_leftUnitor
Mathlib.Tactic.Monoidal.naturality_id
Mathlib.Tactic.Monoidal.naturality_whiskerRight
Mathlib.Tactic.Monoidal.naturality_inv
braiding_leftUnitor_auxā‚‚ šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
MonoidalCategoryStruct.whiskerRight
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.leftUnitor
MonoidalCategoryStruct.rightUnitor
—MonoidalCategory.whiskerRight_id
Category.assoc
Iso.inv_hom_id_assoc
Iso.hom_inv_id_assoc
MonoidalCategory.id_whiskerLeft
BraidedCategory.braiding_tensor_right_hom
braiding_leftUnitor_aux₁
BraidedCategory.braiding_naturality_right
Iso.hom_inv_id
Category.comp_id
MonoidalCategory.triangle
braiding_rightUnitor šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.rightUnitor
MonoidalCategoryStruct.leftUnitor
—MonoidalCategory.whiskerLeft_iff
MonoidalCategory.whiskerLeft_comp
braiding_rightUnitor_auxā‚‚
braiding_rightUnitor_assoc šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.rightUnitor
MonoidalCategoryStruct.leftUnitor
—Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_rightUnitor
braiding_rightUnitor_aux₁ šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.inv
MonoidalCategoryStruct.associator
MonoidalCategoryStruct.whiskerRight
BraidedCategory.braiding
Iso.hom
MonoidalCategoryStruct.whiskerLeft
MonoidalCategoryStruct.rightUnitor
—MonoidalCategory.whiskerRight_id
MonoidalCategory.whiskerLeft_rightUnitor
Iso.hom_inv_id_assoc
Category.assoc
Iso.inv_hom_id
Category.comp_id
braiding_rightUnitor_auxā‚‚ šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
MonoidalCategoryStruct.whiskerLeft
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.rightUnitor
MonoidalCategoryStruct.leftUnitor
—MonoidalCategory.id_whiskerLeft
MonoidalCategory.whiskerLeft_rightUnitor
Category.assoc
Iso.hom_inv_id_assoc
MonoidalCategory.whiskerRight_id
Iso.inv_hom_id
Category.comp_id
Iso.inv_hom_id_assoc
Iso.hom_inv_id
BraidedCategory.hexagon_reverse
BraidedCategory.braiding_tensor_left_hom
BraidedCategory.braiding_naturality_left
MonoidalCategory.triangle_assoc_comp_right
braiding_tensorUnit_left šŸ“–mathematical—Iso.hom
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
BraidedCategory.braiding
CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.leftUnitor
Iso.inv
MonoidalCategoryStruct.rightUnitor
—Category.assoc
Iso.hom_inv_id
Category.comp_id
braiding_tensorUnit_left_assoc šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.leftUnitor
Iso.inv
MonoidalCategoryStruct.rightUnitor
—Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_tensorUnit_left
braiding_tensorUnit_right šŸ“–mathematical—Iso.hom
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
BraidedCategory.braiding
CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.rightUnitor
Iso.inv
MonoidalCategoryStruct.leftUnitor
—Iso.hom_inv_id_assoc
braiding_tensorUnit_right_assoc šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.rightUnitor
Iso.inv
MonoidalCategoryStruct.leftUnitor
—Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_tensorUnit_right
leftUnitor_inv_braiding šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.inv
MonoidalCategoryStruct.leftUnitor
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.rightUnitor
—braiding_tensorUnit_left
Iso.inv_hom_id_assoc
leftUnitor_inv_braiding_assoc šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.inv
MonoidalCategoryStruct.leftUnitor
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.rightUnitor
—Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
leftUnitor_inv_braiding
op_braiding šŸ“–mathematical—Iso.op
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
BraidedCategory.braiding
Opposite
Category.opposite
monoidalCategoryOp
instBraidedCategoryOpposite
Opposite.op
——
op_hom_braiding šŸ“–mathematical—Quiver.Hom.op
CategoryStruct.toQuiver
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
Iso.hom
BraidedCategory.braiding
Opposite
Category.opposite
monoidalCategoryOp
Opposite.op
instBraidedCategoryOpposite
——
op_inv_braiding šŸ“–mathematical—Quiver.Hom.op
CategoryStruct.toQuiver
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
Iso.inv
BraidedCategory.braiding
Opposite
Category.opposite
monoidalCategoryOp
Opposite.op
instBraidedCategoryOpposite
——
rightUnitor_inv_braiding šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.inv
MonoidalCategoryStruct.rightUnitor
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.leftUnitor
—cancel_mono
IsSplitMono.mono
IsSplitMono.of_iso
Iso.isIso_hom
Category.assoc
braiding_leftUnitor
Iso.inv_hom_id
rightUnitor_inv_braiding_assoc šŸ“–mathematical—CategoryStruct.comp
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
MonoidalCategory.toMonoidalCategoryStruct
MonoidalCategoryStruct.tensorUnit
Iso.inv
MonoidalCategoryStruct.rightUnitor
Iso.hom
BraidedCategory.braiding
MonoidalCategoryStruct.leftUnitor
—Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
rightUnitor_inv_braiding
unop_braiding šŸ“–mathematical—Iso.unop
MonoidalCategoryStruct.tensorObj
Opposite
Category.opposite
MonoidalCategory.toMonoidalCategoryStruct
monoidalCategoryOp
BraidedCategory.braiding
instBraidedCategoryOpposite
Opposite.unop
——
unop_hom_braiding šŸ“–mathematical—Quiver.Hom.unop
CategoryStruct.toQuiver
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
Opposite
Category.opposite
MonoidalCategory.toMonoidalCategoryStruct
monoidalCategoryOp
Iso.hom
BraidedCategory.braiding
instBraidedCategoryOpposite
Opposite.unop
——
unop_inv_braiding šŸ“–mathematical—Quiver.Hom.unop
CategoryStruct.toQuiver
Category.toCategoryStruct
MonoidalCategoryStruct.tensorObj
Opposite
Category.opposite
MonoidalCategory.toMonoidalCategoryStruct
monoidalCategoryOp
Iso.inv
BraidedCategory.braiding
instBraidedCategoryOpposite
Opposite.unop
——

CategoryTheory.BraidedCategory

Definitions

NameCategoryTheorems
braiding šŸ“–CompOp
164 mathmath: braiding_naturality_right, CategoryTheory.MonoidalCategory.DayConvolution.braidingHomCorepresenting_app, ModuleCat.MonoidalCategory.braiding_hom_apply, yang_baxter', braiding_tensor_right_hom, CategoryTheory.MonoidalOpposite.unmop_hom_braiding, CategoryTheory.MonoidalOpposite.unmopFunctor_Ī“, braiding_tensor_right_hom_assoc, CommAlgCat.braiding_hom_hom, CategoryTheory.MonObj.instIsMonHomHomBraiding, braiding_tensor_left_inv, CategoryTheory.braiding_tensorUnit_left_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd_assoc, hexagon_reverse_assoc, braiding_inv_naturality_assoc, CategoryTheory.Functor.LaxBraided.braided, curriedBraidingNatIso_inv_app_app, CategoryTheory.Over.braiding_inv_left, CategoryTheory.rightUnitor_inv_braiding, CategoryTheory.Pi.braiding_inv_apply, CategoryTheory.symmetricOfHasFiniteProducts_braiding_hom, CategoryTheory.HopfObj.mul_antipode, braiding_tensor_left_hom, CategoryTheory.braiding_inv_tensorUnit_right_assoc, CategoryTheory.CartesianMonoidalCategory.lift_braiding_hom, CategoryTheory.Bimon.compatibility_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_inv_fst_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst, CategoryTheory.leftUnitor_inv_braiding_assoc, CategoryTheory.braiding_rightUnitor_aux₁, CategoryTheory.coprodComparison_tensorRight_braiding_hom, CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv, CategoryTheory.op_inv_braiding, braiding_tensor_left_inv_assoc, CategoryTheory.GrpObj.tensorHom_inv_inv_mul_assoc, CategoryTheory.symmetricOfHasFiniteCoproducts_braiding, braiding_naturality, hexagon_reverse_inv, curriedBraidingNatIso_hom_app_app, CategoryTheory.HopfObj.antipode_comul, CategoryTheory.braiding_hom_apply, CategoryTheory.MonoidalOpposite.mop_inv_braiding, yang_baxter, braiding_naturality_left, hexagon_forward_iso, yang_baxter_iso, hexagon_forward_inv_assoc, hexagon_reverse, CategoryTheory.HopfObj.antipode_comulā‚‚, braiding_tensor_left_hom_assoc, braiding_inv_naturality_right_assoc, CategoryTheory.SymmetricCategory.braiding_swap_eq_inv_braiding, CategoryTheory.op_braiding, CategoryTheory.Functor.Braided.braided, yang_baxter_assoc, CategoryTheory.Center.ofBraidedObj_snd_β, CategoryTheory.Grp.braiding_inv_hom, CategoryTheory.braiding_rightUnitor_assoc, SemimoduleCat.MonoidalCategory.braiding_hom_apply, braiding_naturality_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app, SemimoduleCat.MonoidalCategory.braiding_inv_apply, CategoryTheory.eComp_op_eq_assoc, CategoryTheory.braiding_leftUnitor_auxā‚‚, CategoryTheory.braiding_tensorUnit_left, CategoryTheory.rightUnitor_inv_braiding_assoc, hexagon_forward, hexagon_reverse_iso, CategoryTheory.braiding_tensorUnit_right_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_inv_snd, CategoryTheory.SymmetricCategory.symmetry_assoc, CategoryTheory.op_hom_braiding, CategoryTheory.Functor.map_braiding_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app, CategoryTheory.unop_braiding, tensorLeftIsoTensorRight_hom_app, CategoryTheory.MonoidalCategory.DayConvolution.braidingInvCorepresenting_app, CategoryTheory.MonObj.one_braiding, CategoryTheory.MonoidalCategory.externalProductFlip_hom_app_app_app_app, CategoryTheory.CartesianMonoidalCategory.lift_braiding_hom_assoc, CategoryTheory.tensorHom_eComp_op_eq_assoc, CategoryTheory.IsCommMonObj.mul_comm'_assoc, CategoryTheory.HopfObj.mul_antipode₁, CommAlgCat.braiding_inv_hom, CategoryTheory.Grp.braiding_inv_hom_hom, CategoryTheory.CartesianMonoidalCategory.braiding_hom_fst_assoc, CategoryTheory.CartesianMonoidalCategory.braiding_inv_fst, CategoryTheory.braiding_rightUnitor_auxā‚‚, CategoryTheory.SymmetricCategory.symmetry, CategoryTheory.tensorHom_eComp_op_eq, CategoryTheory.GrpObj.mul_inv_rev_assoc, CategoryTheory.braiding_rightUnitor, CategoryTheory.SymmetricCategory.rightDistrib_of_leftDistrib, CategoryTheory.IsCommComonObj.comul_comm_assoc, CategoryTheory.MonoidalOpposite.mopFunctor_μ, CategoryTheory.braiding_inv_tensorUnit_left_assoc, braiding_inv_naturality_left_assoc, CategoryTheory.GrpObj.tensorHom_inv_inv_mul, CategoryTheory.braiding_leftUnitor_assoc, CategoryTheory.GrpObj.mul_inv, CategoryTheory.IsCommMonObj.mul_comm, CategoryTheory.unop_inv_braiding, CategoryTheory.braiding_inv_tensorUnit_right, CategoryTheory.MonoidalOpposite.unmopFunctor_μ, CategoryTheory.MonObj.mul_braiding, CategoryTheory.GrpObj.mul_inv_rev, CategoryTheory.braiding_leftUnitor, braiding_naturality_left_assoc, CategoryTheory.MonoidalOpposite.mop_hom_braiding, CategoryTheory.MonoidalCategory.externalProductSwap_inv_app_app, hexagon_reverse_inv_assoc, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_hom_app_assoc, CategoryTheory.Mon.braiding_inv_hom, CategoryTheory.HopfObj.antipode_comul₁, CategoryTheory.symmetricOfHasFiniteProducts_braiding_inv, CategoryTheory.MonoidalOpposite.unmop_inv_braiding, CategoryTheory.Localization.Monoidal.β_hom_app, CategoryTheory.GrpObj.mul_inv_assoc, CategoryTheory.IsCommMonObj.mul_comm_assoc, CategoryTheory.Over.braiding_hom_left, CategoryTheory.Localization.Monoidal.braidingNatIso_hom_app, CategoryTheory.braiding_tensorUnit_right, braiding_inv_naturality_left, CategoryTheory.IsCommComonObj.comul_comm, Action.β_inv_hom, CategoryTheory.braiding_leftUnitor_aux₁, CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_comp_assoc, CategoryTheory.HopfObj.mul_antipodeā‚‚, CategoryTheory.MonoidalOpposite.mop_braiding, CategoryTheory.leftUnitor_inv_braiding, CategoryTheory.unop_hom_braiding, CategoryTheory.IsCommMonObj.mul_comm', hexagon_forward_inv, CategoryTheory.Grp.braiding_hom_hom, CategoryTheory.CartesianMonoidalCategory.braiding_inv_snd_assoc, CategoryTheory.coprodComparison_tensorLeft_braiding_hom, CategoryTheory.Pi.isoApp_braiding, CategoryTheory.CartesianMonoidalCategory.lift_snd_comp_fst_comp, CategoryTheory.MonoidalCategory.DayConvolution.unit_app_braiding_inv_app_assoc, CategoryTheory.MonoidalCategory.externalProductSwap_hom_app_app, braiding_inv_naturality_right, CategoryTheory.braiding_inv_apply, CategoryTheory.Functor.LaxBraided.braided_assoc, CategoryTheory.Mon.braiding_hom_hom, ModuleCat.MonoidalCategory.braiding_inv_apply, CategoryTheory.MonoidalOpposite.mopFunctor_Ī“, braiding_inv_naturality, CategoryTheory.CartesianMonoidalCategory.lift_snd_fst, CategoryTheory.Pi.braiding_hom_apply, CategoryTheory.Bimon.compatibility, CategoryTheory.eComp_op_eq, CategoryTheory.braiding_inv_tensorUnit_left, braiding_tensor_right_inv_assoc, CategoryTheory.MonoidalOpposite.unmop_braiding, CategoryTheory.CartesianMonoidalCategory.braiding_hom_snd, CategoryTheory.Grp.braiding_hom_hom_hom, CategoryTheory.Functor.map_braiding, braiding_naturality_right_assoc, CategoryTheory.MonoidalCategory.externalProductFlip_inv_app_app_app_app, Action.β_hom_hom, hexagon_forward_assoc, braiding_tensor_right_inv, tensorLeftIsoTensorRight_inv_app, CategoryTheory.CartesianMonoidalCategory.lift_braiding_inv_assoc
curriedBraidingNatIso šŸ“–CompOp
2 mathmath: curriedBraidingNatIso_inv_app_app, curriedBraidingNatIso_hom_app_app
ofFaithful šŸ“–CompOp—
ofFullyFaithful šŸ“–CompOp—
tensorLeftIsoTensorRight šŸ“–CompOp
2 mathmath: tensorLeftIsoTensorRight_hom_app, tensorLeftIsoTensorRight_inv_app

Theorems

NameKindAssumesProvesValidatesDepends On
braiding_inv_naturality šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.inv
braiding
—CategoryTheory.CommSq.w
CategoryTheory.CommSq.vert_inv
braiding_naturality
braiding_inv_naturality_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.inv
braiding
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_inv_naturality
braiding_inv_naturality_left šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.inv
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.CommSq.w
CategoryTheory.CommSq.vert_inv
braiding_naturality_right
braiding_inv_naturality_left_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.inv
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_inv_naturality_left
braiding_inv_naturality_right šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—CategoryTheory.CommSq.w
CategoryTheory.CommSq.vert_inv
braiding_naturality_left
braiding_inv_naturality_right_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_inv_naturality_right
braiding_naturality šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.hom
braiding
—CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.Category.assoc
braiding_naturality_left
braiding_naturality_right_assoc
braiding_naturality_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.hom
braiding
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_naturality
braiding_naturality_left šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.hom
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
——
braiding_naturality_left_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.hom
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_naturality_left
braiding_naturality_right šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.hom
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerRight
——
braiding_naturality_right_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.hom
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_naturality_right
braiding_tensor_left_hom šŸ“–mathematical—CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
braiding
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—CategoryTheory.cancel_epi
CategoryTheory.IsSplitEpi.epi
CategoryTheory.IsSplitEpi.of_iso
CategoryTheory.Iso.isIso_inv
CategoryTheory.cancel_mono
CategoryTheory.IsSplitMono.mono
CategoryTheory.IsSplitMono.of_iso
CategoryTheory.Category.assoc
hexagon_reverse
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.Iso.hom_inv_id
CategoryTheory.Category.comp_id
braiding_tensor_left_hom_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
braiding
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_tensor_left_hom
braiding_tensor_left_inv šŸ“–mathematical—CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
braiding
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.eq_of_inv_eq_inv
CategoryTheory.Iso.isIso_inv
CategoryTheory.IsIso.comp_isIso
CategoryTheory.MonoidalCategory.whiskerRight_isIso
CategoryTheory.Iso.isIso_hom
CategoryTheory.MonoidalCategory.whiskerLeft_isIso
CategoryTheory.IsIso.Iso.inv_inv
braiding_tensor_left_hom
CategoryTheory.IsIso.inv_comp
CategoryTheory.MonoidalCategory.inv_whiskerLeft
CategoryTheory.IsIso.Iso.inv_hom
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.inv_whiskerRight
braiding_tensor_left_inv_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
braiding
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_tensor_left_inv
braiding_tensor_right_hom šŸ“–mathematical—CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
braiding
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.cancel_epi
CategoryTheory.IsSplitEpi.epi
CategoryTheory.IsSplitEpi.of_iso
CategoryTheory.Iso.isIso_hom
CategoryTheory.cancel_mono
CategoryTheory.IsSplitMono.mono
CategoryTheory.IsSplitMono.of_iso
CategoryTheory.Category.assoc
hexagon_forward
CategoryTheory.Iso.hom_inv_id_assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
braiding_tensor_right_hom_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
braiding
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_tensor_right_hom
braiding_tensor_right_inv šŸ“–mathematical—CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
braiding
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—CategoryTheory.eq_of_inv_eq_inv
CategoryTheory.Iso.isIso_inv
CategoryTheory.IsIso.comp_isIso
CategoryTheory.Iso.isIso_hom
CategoryTheory.MonoidalCategory.whiskerLeft_isIso
CategoryTheory.MonoidalCategory.whiskerRight_isIso
CategoryTheory.IsIso.Iso.inv_inv
braiding_tensor_right_hom
CategoryTheory.IsIso.inv_comp
CategoryTheory.IsIso.Iso.inv_hom
CategoryTheory.MonoidalCategory.inv_whiskerRight
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.inv_whiskerLeft
braiding_tensor_right_inv_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
braiding
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braiding_tensor_right_inv
curriedBraidingNatIso_hom_app_app šŸ“–mathematical—CategoryTheory.NatTrans.app
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.MonoidalCategory.curriedTensor
CategoryTheory.Functor.flip
CategoryTheory.Iso.hom
curriedBraidingNatIso
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
braiding
——
curriedBraidingNatIso_inv_app_app šŸ“–mathematical—CategoryTheory.NatTrans.app
CategoryTheory.Functor.obj
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.Functor.flip
CategoryTheory.MonoidalCategory.curriedTensor
CategoryTheory.Iso.inv
curriedBraidingNatIso
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
braiding
——
hexagon_forward šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
——
hexagon_forward_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
hexagon_forward
hexagon_forward_inv šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—braiding_tensor_right_inv
CategoryTheory.Category.assoc
CategoryTheory.Iso.hom_inv_id
CategoryTheory.Category.comp_id
CategoryTheory.Iso.inv_hom_id_assoc
hexagon_forward_inv_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
hexagon_forward_inv
hexagon_forward_iso šŸ“–mathematical—CategoryTheory.Iso.trans
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.associator
braiding
CategoryTheory.MonoidalCategory.whiskerRightIso
CategoryTheory.MonoidalCategory.whiskerLeftIso
—CategoryTheory.Iso.ext
hexagon_forward
hexagon_reverse šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.Iso.hom
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategoryStruct.whiskerRight
——
hexagon_reverse_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.Iso.hom
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
hexagon_reverse
hexagon_reverse_inv šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.Iso.inv
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—braiding_tensor_left_inv
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
CategoryTheory.Iso.hom_inv_id_assoc
hexagon_reverse_inv_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.Iso.inv
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
hexagon_reverse_inv
hexagon_reverse_iso šŸ“–mathematical—CategoryTheory.Iso.trans
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.symm
CategoryTheory.MonoidalCategoryStruct.associator
braiding
CategoryTheory.MonoidalCategory.whiskerLeftIso
CategoryTheory.MonoidalCategory.whiskerRightIso
—CategoryTheory.Iso.ext
hexagon_reverse
tensorLeftIsoTensorRight_hom_app šŸ“–mathematical—CategoryTheory.NatTrans.app
CategoryTheory.MonoidalCategory.tensorLeft
CategoryTheory.MonoidalCategory.tensorRight
CategoryTheory.Iso.hom
CategoryTheory.Functor
CategoryTheory.Functor.category
tensorLeftIsoTensorRight
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
braiding
——
tensorLeftIsoTensorRight_inv_app šŸ“–mathematical—CategoryTheory.NatTrans.app
CategoryTheory.MonoidalCategory.tensorRight
CategoryTheory.MonoidalCategory.tensorLeft
CategoryTheory.Iso.inv
CategoryTheory.Functor
CategoryTheory.Functor.category
tensorLeftIsoTensorRight
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
braiding
——
yang_baxter šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.hom
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—braiding_tensor_right_hom_assoc
CategoryTheory.cancel_mono
CategoryTheory.IsSplitMono.mono
CategoryTheory.IsSplitMono.of_iso
CategoryTheory.Iso.isIso_inv
CategoryTheory.Category.assoc
CategoryTheory.Iso.hom_inv_id
CategoryTheory.Category.comp_id
braiding_naturality_right
braiding_tensor_right_hom
yang_baxter' šŸ“–mathematical—CategoryTheory.monoidalComp
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCoherence.assoc
CategoryTheory.MonoidalCoherence.whiskerRight
CategoryTheory.MonoidalCoherence.refl
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.hom
braiding
CategoryTheory.MonoidalCoherence.assoc'
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
—CategoryTheory.cancel_epi
CategoryTheory.IsSplitEpi.epi
CategoryTheory.IsSplitEpi.of_iso
CategoryTheory.Iso.isIso_inv
CategoryTheory.cancel_mono
CategoryTheory.IsSplitMono.mono
CategoryTheory.IsSplitMono.of_iso
CategoryTheory.Iso.isIso_hom
Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_monoidalComp
Mathlib.Tactic.Monoidal.eval_whiskerRight
Mathlib.Tactic.Monoidal.eval_of
Mathlib.Tactic.Monoidal.evalWhiskerRight_cons_of_of
Mathlib.Tactic.Monoidal.evalWhiskerRight_nil
Mathlib.Tactic.Monoidal.evalWhiskerRightAux_of
Mathlib.Tactic.Monoidal.evalComp_cons
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.evalComp_nil_cons
Mathlib.Tactic.Monoidal.eval_whiskerLeft
Mathlib.Tactic.Monoidal.evalWhiskerLeft_of_cons
Mathlib.Tactic.Monoidal.evalWhiskerLeft_nil
Mathlib.Tactic.BicategoryLike.mk_eq_of_cons
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_associator
Mathlib.Tactic.Monoidal.naturality_whiskerRight
Mathlib.Tactic.Monoidal.naturality_id
Mathlib.Tactic.Monoidal.naturality_whiskerLeft
yang_baxter
yang_baxter_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.hom
braiding
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
yang_baxter
yang_baxter_iso šŸ“–mathematical—CategoryTheory.Iso.trans
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.symm
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategory.whiskerRightIso
braiding
CategoryTheory.MonoidalCategory.whiskerLeftIso
—CategoryTheory.Iso.ext
yang_baxter

CategoryTheory.Discrete

Definitions

NameCategoryTheorems
monoidalFunctorBraided šŸ“–CompOp—

CategoryTheory.Functor

Definitions

NameCategoryTheorems
LaxBraided šŸ“–CompData—

Theorems

NameKindAssumesProvesValidatesDepends On
map_braiding šŸ“–mathematical—map
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
obj
OplaxMonoidal.Ī“
Monoidal.toOplaxMonoidal
Braided.toMonoidal
LaxMonoidal.μ
LaxBraided.toLaxMonoidal
Braided.toLaxBraided
—Braided.braided
Monoidal.Γ_μ_assoc
map_braiding_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
obj
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
map
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
OplaxMonoidal.Ī“
Monoidal.toOplaxMonoidal
Braided.toMonoidal
LaxMonoidal.μ
LaxBraided.toLaxMonoidal
Braided.toLaxBraided
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
map_braiding

CategoryTheory.Functor.Braided

Definitions

NameCategoryTheorems
instComp šŸ“–CompOp
8 mathmath: CategoryTheory.Functor.mapCommGrpCompIso_inv_app_hom_hom_hom, CategoryTheory.Functor.mapCommGrpCompIso_hom_app_hom_hom_hom, CategoryTheory.Adjunction.mapCommGrp_unit, CategoryTheory.Equivalence.mapCommGrp_unitIso, CategoryTheory.Functor.comp_mapCommGrp_mul, CategoryTheory.Functor.comp_mapCommGrp_one, CategoryTheory.Equivalence.mapCommGrp_counitIso, CategoryTheory.Adjunction.mapCommGrp_counit
instId šŸ“–CompOp
8 mathmath: CategoryTheory.Adjunction.mapCommGrp_unit, CategoryTheory.Equivalence.mapCommGrp_unitIso, CategoryTheory.Functor.mapCommGrp_id_one, CategoryTheory.Functor.mapCommGrpIdIso_hom_app_hom_hom_hom, CategoryTheory.Functor.mapCommpGrp_id_mul, CategoryTheory.Functor.mapCommGrpIdIso_inv_app_hom_hom_hom, CategoryTheory.Equivalence.mapCommGrp_counitIso, CategoryTheory.Adjunction.mapCommGrp_counit
toLaxBraided šŸ“–CompOp
27 mathmath: CategoryTheory.Over.μ_pullback_left_snd', CategoryTheory.Equivalence.mapCommMon_inverse, CategoryTheory.Over.monObjMkPullbackSnd_mul, CategoryTheory.Adjunction.mapCommMon_unit, CategoryTheory.Adjunction.mapCommMon_counit, CommGrpCat.μ_forget_apply, CategoryTheory.Over.μ_pullback_left_fst_snd', CategoryTheory.Equivalence.mapCommMon_unitIso, CategoryTheory.Functor.comp_mapCommGrp_mul, AddCommGrpCat.μ_forget_apply, CategoryTheory.Over.μ_pullback_left_fst_fst', CategoryTheory.Over.μ_pullback_left_fst_snd, CategoryTheory.Over.monObjMkPullbackSnd_one, CategoryTheory.Functor.map_braiding_assoc, CategoryTheory.Functor.Full.mapCommMon, AddGrpCat.μ_forget_apply, AlgebraicGeometry.Scheme.monObjAsOverPullback_mul, CategoryTheory.Functor.FullyFaithful.mapCommMon_preimage, CategoryTheory.Equivalence.mapCommMon_counitIso, CategoryTheory.Functor.comp_mapCommGrp_one, CategoryTheory.Over.μ_pullback_left_snd, CategoryTheory.Over.μ_pullback_left_fst_fst, AlgebraicGeometry.Scheme.monObjAsOverPullback_one, CategoryTheory.Over.ε_pullback_left, GrpCat.μ_forget_apply, CategoryTheory.Equivalence.mapCommMon_functor, CategoryTheory.Functor.map_braiding
toMonoidal šŸ“–CompOp
13 mathmath: ext_iff, CategoryTheory.Functor.mapCommGrp_obj_grp_one, toMonoidal_injective, braided, CategoryTheory.Functor.map_braiding_assoc, CategoryTheory.Functor.FullyFaithful.mapCommMon_preimage, CategoryTheory.Over.Ī·_pullback_left, CategoryTheory.Functor.FullyFaithful.mapCommGrp_preimage, CategoryTheory.Functor.mapCommGrp_map_hom_hom_hom, CategoryTheory.Functor.mapCommGrpNatTrans_app_hom_hom_hom, CategoryTheory.Functor.mapCommGrp_obj_grp_mul, CategoryTheory.Functor.map_braiding, CategoryTheory.Functor.mapCommGrp_obj_grp_inv

Theorems

NameKindAssumesProvesValidatesDepends On
braided šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Functor.Monoidal.toLaxMonoidal
toMonoidal
CategoryTheory.Functor.map
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
——
ext šŸ“–ā€”CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Functor.Monoidal.toLaxMonoidal
toMonoidal
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Functor.OplaxMonoidal.Ī·
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
CategoryTheory.Functor.OplaxMonoidal.Ī“
———
ext_iff šŸ“–mathematical—CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Functor.Monoidal.toLaxMonoidal
toMonoidal
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Functor.OplaxMonoidal.Ī·
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
CategoryTheory.Functor.OplaxMonoidal.Ī“
—ext
toMonoidal_injective šŸ“–mathematical—CategoryTheory.Functor.Braided
CategoryTheory.Functor.Monoidal
toMonoidal
——

CategoryTheory.Functor.LaxBraided

Definitions

NameCategoryTheorems
id šŸ“–CompOp
8 mathmath: CategoryTheory.Adjunction.mapCommMon_unit, CategoryTheory.Adjunction.mapCommMon_counit, CategoryTheory.Functor.mapCommMonIdIso_hom_app_hom_hom, CategoryTheory.Equivalence.mapCommMon_unitIso, CategoryTheory.Functor.mapCommMon_id_mul, CategoryTheory.Equivalence.mapCommMon_counitIso, CategoryTheory.Functor.mapCommMonIdIso_inv_app_hom_hom, CategoryTheory.Functor.mapCommMon_id_one
instComp šŸ“–CompOp
8 mathmath: CategoryTheory.Adjunction.mapCommMon_unit, CategoryTheory.Adjunction.mapCommMon_counit, CategoryTheory.Functor.mapCommMonCompIso_inv_app_hom_hom, CategoryTheory.Functor.comp_mapCommMon_mul, CategoryTheory.Equivalence.mapCommMon_unitIso, CategoryTheory.Equivalence.mapCommMon_counitIso, CategoryTheory.Functor.comp_mapCommMon_one, CategoryTheory.Functor.mapCommMonCompIso_hom_app_hom_hom
ofNatIso šŸ“–CompOp—
toLaxMonoidal šŸ“–CompOp
30 mathmath: CategoryTheory.Over.μ_pullback_left_snd', CategoryTheory.Functor.mapCommMon_obj_mon_mul, CategoryTheory.Over.monObjMkPullbackSnd_mul, braided, CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ_assoc, CommGrpCat.μ_forget_apply, CategoryTheory.Functor.instIsMonHomμ, CategoryTheory.MonoidalCategory.tensorμ_comp_μ_tensorHom_μ_comp_μ, CategoryTheory.Over.μ_pullback_left_fst_snd', CategoryTheory.Functor.comp_mapCommMon_mul, CategoryTheory.Functor.isCommMonObj_obj, CategoryTheory.Functor.comp_mapCommGrp_mul, AddCommGrpCat.μ_forget_apply, CategoryTheory.Over.μ_pullback_left_fst_fst', CategoryTheory.Over.μ_pullback_left_fst_snd, CategoryTheory.Over.monObjMkPullbackSnd_one, CategoryTheory.Functor.map_braiding_assoc, AddGrpCat.μ_forget_apply, AlgebraicGeometry.Scheme.monObjAsOverPullback_mul, CategoryTheory.Functor.mapCommMon_map_hom_hom, CategoryTheory.Functor.mapCommMon_obj_mon_one, CategoryTheory.Functor.comp_mapCommGrp_one, CategoryTheory.Over.μ_pullback_left_snd, CategoryTheory.Over.μ_pullback_left_fst_fst, AlgebraicGeometry.Scheme.monObjAsOverPullback_one, braided_assoc, CategoryTheory.Over.ε_pullback_left, GrpCat.μ_forget_apply, CategoryTheory.Functor.map_braiding, CategoryTheory.Functor.comp_mapCommMon_one

Theorems

NameKindAssumesProvesValidatesDepends On
braided šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Functor.LaxMonoidal.μ
toLaxMonoidal
CategoryTheory.Functor.map
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
——
braided_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.Functor.LaxMonoidal.μ
toLaxMonoidal
CategoryTheory.Functor.map
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
braided

CategoryTheory.LaxBraidedFunctor

Definitions

NameCategoryTheorems
forget šŸ“–CompOp
4 mathmath: CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, forget_map, forget_obj, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app
fullyFaithfulForget šŸ“–CompOp—
homMk šŸ“–CompOp
3 mathmath: isoMk_inv, isoMk_hom, homMk_hom_hom
instCategory šŸ“–CompOp
27 mathmath: isoMk_inv, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_map, isoOfComponents_inv_hom_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, comp_hom, isoOfComponents_hom_hom_app, forget_map, CategoryTheory.CommMon.equivLaxBraidedFunctorPUnit_unitIso, CategoryTheory.CommMon.equivLaxBraidedFunctorPUnit_functor, isoOfComponents_hom_hom_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_obj, CategoryTheory.Functor.mapCommMonFunctor_map_app, comp_hom_assoc, CategoryTheory.Functor.mapCommMonFunctor_obj, isoMk_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_obj, forget_obj, CategoryTheory.CommMon.equivLaxBraidedFunctorPUnit_inverse, isoOfComponents_inv_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_one, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_inv_app_hom_hom, id_hom, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_aux_mul, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.counitIso_hom_app_hom_hom, CategoryTheory.CommMon.equivLaxBraidedFunctorPUnit_counitIso
isoMk šŸ“–CompOp
2 mathmath: isoMk_inv, isoMk_hom
isoOfComponents šŸ“–CompOp
4 mathmath: isoOfComponents_inv_hom_hom_app, isoOfComponents_hom_hom_app, isoOfComponents_hom_hom_hom_app, isoOfComponents_inv_hom_app
laxBraided šŸ“–CompOp
3 mathmath: CategoryTheory.Functor.mapCommMonFunctor_map_app, CategoryTheory.Functor.mapCommMonFunctor_obj, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_obj
of šŸ“–CompOp
3 mathmath: CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_obj, of_toFunctor
toFunctor šŸ“–CompOp
9 mathmath: isoMk_inv, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, CategoryTheory.Functor.mapCommMonFunctor_map_app, CategoryTheory.Functor.mapCommMonFunctor_obj, isoMk_hom, of_toFunctor, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.laxBraidedToCommMon_obj, toLaxMonoidalFunctor_toFunctor, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app
toLaxMonoidalFunctor šŸ“–CompOp
16 mathmath: isoOfComponents_inv_hom_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_hom_app_hom_hom_app, comp_hom, isoOfComponents_hom_hom_app, forget_map, isoOfComponents_hom_hom_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.commMonToLaxBraided_map_hom_hom_app, CategoryTheory.Functor.mapCommMonFunctor_map_app, comp_hom_assoc, homMk_hom_hom, toLaxMonoidalFunctor_toFunctor, forget_obj, isoOfComponents_inv_hom_app, CategoryTheory.CommMon.EquivLaxBraidedFunctorPUnit.unitIso_inv_app_hom_hom_app, id_hom, hom_ext_iff

Theorems

NameKindAssumesProvesValidatesDepends On
comp_hom šŸ“–mathematical—CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.LaxBraidedFunctor
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
toLaxMonoidalFunctor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
instCategory
——
comp_hom_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.Category.toCategoryStruct
CategoryTheory.LaxMonoidalFunctor.instCategory
toLaxMonoidalFunctor
CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.LaxBraidedFunctor
instCategory
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_hom
forget_map šŸ“–mathematical—CategoryTheory.Functor.map
CategoryTheory.LaxBraidedFunctor
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
forget
CategoryTheory.InducedCategory.Hom.hom
toLaxMonoidalFunctor
——
forget_obj šŸ“–mathematical—CategoryTheory.Functor.obj
CategoryTheory.LaxBraidedFunctor
instCategory
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
forget
toLaxMonoidalFunctor
——
homMk_hom_hom šŸ“–mathematical—CategoryTheory.LaxMonoidalFunctor.Hom.hom
toLaxMonoidalFunctor
CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.LaxBraidedFunctor
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
homMk
——
hom_ext šŸ“–ā€”CategoryTheory.LaxMonoidalFunctor.Hom.hom
toLaxMonoidalFunctor
CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.LaxBraidedFunctor
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
——CategoryTheory.InducedCategory.hom_ext
CategoryTheory.LaxMonoidalFunctor.hom_ext
hom_ext_iff šŸ“–mathematical—CategoryTheory.LaxMonoidalFunctor.Hom.hom
toLaxMonoidalFunctor
CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.LaxBraidedFunctor
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
—hom_ext
id_hom šŸ“–mathematical—CategoryTheory.LaxMonoidalFunctor.Hom.hom
toLaxMonoidalFunctor
CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.LaxBraidedFunctor
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
instCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.LaxMonoidalFunctor.toFunctor
——
isoMk_hom šŸ“–mathematical—CategoryTheory.Iso.hom
CategoryTheory.LaxBraidedFunctor
instCategory
isoMk
homMk
CategoryTheory.Functor
CategoryTheory.Functor.category
toFunctor
——
isoMk_inv šŸ“–mathematical—CategoryTheory.Iso.inv
CategoryTheory.LaxBraidedFunctor
instCategory
isoMk
homMk
CategoryTheory.Functor
CategoryTheory.Functor.category
toFunctor
——
isoOfComponents_hom_hom_app šŸ“–mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
toFunctor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Functor.LaxBraided.toLaxMonoidal
laxBraided
CategoryTheory.Iso.hom
CategoryTheory.NatTrans.app
CategoryTheory.LaxMonoidalFunctor.toFunctor
toLaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.LaxBraidedFunctor
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
instCategory
isoOfComponents
—isoOfComponents_hom_hom_hom_app
isoOfComponents_hom_hom_hom_app šŸ“–mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
toFunctor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Functor.LaxBraided.toLaxMonoidal
laxBraided
CategoryTheory.Iso.hom
CategoryTheory.NatTrans.app
CategoryTheory.LaxMonoidalFunctor.toFunctor
toLaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.LaxBraidedFunctor
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
instCategory
isoOfComponents
——
isoOfComponents_inv_hom_app šŸ“–mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
toFunctor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Functor.LaxBraided.toLaxMonoidal
laxBraided
CategoryTheory.Iso.hom
CategoryTheory.NatTrans.app
CategoryTheory.LaxMonoidalFunctor.toFunctor
toLaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.LaxBraidedFunctor
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Iso.inv
instCategory
isoOfComponents
—isoOfComponents_inv_hom_hom_app
isoOfComponents_inv_hom_hom_app šŸ“–mathematicalQuiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Functor.obj
toFunctor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.Functor.LaxBraided.toLaxMonoidal
laxBraided
CategoryTheory.Iso.hom
CategoryTheory.NatTrans.app
CategoryTheory.LaxMonoidalFunctor.toFunctor
toLaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.Hom.hom
CategoryTheory.InducedCategory.Hom.hom
CategoryTheory.LaxBraidedFunctor
CategoryTheory.LaxMonoidalFunctor
CategoryTheory.LaxMonoidalFunctor.instCategory
CategoryTheory.Iso.inv
instCategory
isoOfComponents
——
of_toFunctor šŸ“–mathematical—toFunctor
of
——
toLaxMonoidalFunctor_toFunctor šŸ“–mathematical—CategoryTheory.LaxMonoidalFunctor.toFunctor
toLaxMonoidalFunctor
toFunctor
——

CategoryTheory.MonoidalCategory

Definitions

NameCategoryTheorems
tensorMonoidal šŸ“–CompOp
4 mathmath: tensor_η, tensor_Γ, tensor_ε, tensor_μ
tensorĪ“ šŸ“–CompOp
12 mathmath: CategoryTheory.CartesianMonoidalCategory.tensorΓ_snd, tensorμ_tensorΓ_assoc, CategoryTheory.CartesianMonoidalCategory.tensorΓ_snd_assoc, CategoryTheory.MonObj.mul_mul_mul_comm'_assoc, tensorμ_tensorΓ, CategoryTheory.CartesianMonoidalCategory.tensorΓ_fst_assoc, CategoryTheory.MonObj.mul_mul_mul_comm', tensorΓ_tensorμ, tensor_Γ, tensorΓ_tensorμ_assoc, CategoryTheory.CartesianMonoidalCategory.tensorΓ_fst, CategoryTheory.Mon_Class.mul_mul_mul_comm'
tensorμ šŸ“–CompOp
54 mathmath: CategoryTheory.Comon.tensorObj_comul', tensor_left_unitality, tensorμ_natural_assoc, tensorμ_tensorΓ_assoc, rightUnitor_monoidal_assoc, CategoryTheory.Comon.tensorObj_comul, tensorμ_natural_right_assoc, tensorμ_natural_right, CategoryTheory.CartesianMonoidalCategory.tensorμ_fst_assoc, tensorμ_comp_μ_tensorHom_μ_comp_μ_assoc, CategoryTheory.CopyDiscardCategory.copy_tensor, CategoryTheory.MonObj.mul_leftUnitor, CategoryTheory.BraidedCategory.unop_tensorμ, tensorμ_tensorΓ, tensorμ_comp_μ_tensorHom_μ_comp_μ, associator_monoidal, CategoryTheory.MonObj.mul_mul_mul_comm, CategoryTheory.MonObj.tensorObj.mul_def, CategoryTheory.CartesianMonoidalCategory.tensorμ_snd, tensor_associativity_assoc, leftUnitor_monoidal, SemimoduleCat.MonoidalCategory.tensorμ_apply, CategoryTheory.BimonObj.mul_comul_assoc, associator_monoidal_assoc, CategoryTheory.Mon.tensorObj_mul, ModuleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, CategoryTheory.MonObj.Mon_tensor_mul_one, CategoryTheory.MonObj.Mon_tensor_one_mul, CategoryTheory.MonObj.Mon_tensor_mul_assoc, ModuleCat.MonoidalCategory.tensorμ_apply, CategoryTheory.MonObj.mul_mul_mul_comm_assoc, tensorΓ_tensorμ, tensorμ_natural, CategoryTheory.MonObj.mul_associator, SemimoduleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, CategoryTheory.Mon.mul_def, tensor_associativity, tensor_right_unitality, tensorμ_natural_left, tensor_left_unitality_assoc, CategoryTheory.BraidedCategory.op_tensorμ, rightUnitor_monoidal, leftUnitor_monoidal_assoc, tensorμ_natural_left_assoc, CategoryTheory.BimonObj.mul_comul, CategoryTheory.CartesianMonoidalCategory.tensorμ_fst, CategoryTheory.MonObj.mul_rightUnitor, tensorΓ_tensorμ_assoc, CategoryTheory.Bimon.Mon_Class.tensorObj.mul_def, tensor_right_unitality_assoc, tensor_μ, CategoryTheory.CartesianMonoidalCategory.tensorμ_snd_assoc, CategoryTheory.Mon_Class.mul_mul_mul_comm, CategoryTheory.Mon.tensor_mul

Theorems

NameKindAssumesProvesValidatesDepends On
associator_monoidal šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
tensorμ
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.BraidedCategory.braiding_tensor_right_hom
Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_whiskerLeft
Mathlib.Tactic.Monoidal.evalWhiskerLeft_nil
Mathlib.Tactic.Monoidal.eval_whiskerRight
Mathlib.Tactic.Monoidal.eval_of
Mathlib.Tactic.Monoidal.evalWhiskerRight_cons_of_of
Mathlib.Tactic.Monoidal.evalWhiskerRight_nil
Mathlib.Tactic.Monoidal.evalWhiskerRightAux_of
Mathlib.Tactic.Monoidal.evalComp_cons
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.evalComp_nil_cons
Mathlib.Tactic.Monoidal.evalWhiskerLeft_of_cons
Mathlib.Tactic.Monoidal.evalWhiskerRight_cons_whisker
Mathlib.Tactic.Monoidal.evalWhiskerLeft_comp
Mathlib.Tactic.Monoidal.evalWhiskerRight_comp
Mathlib.Tactic.Monoidal.eval_monoidalComp
Mathlib.Tactic.BicategoryLike.mk_eq_of_cons
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_associator
Mathlib.Tactic.Monoidal.naturality_whiskerLeft
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_whiskerRight
Mathlib.Tactic.Monoidal.naturality_id
whisker_exchange
CategoryTheory.BraidedCategory.braiding_tensor_left_hom
Mathlib.Tactic.Monoidal.eval_tensorHom
Mathlib.Tactic.Monoidal.evalHorizontalComp_nil_nil
Mathlib.Tactic.Monoidal.naturality_tensorHom
associator_monoidal_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
tensorμ
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
associator_monoidal
leftUnitor_monoidal šŸ“–mathematical—CategoryTheory.MonoidalCategoryStruct.tensorHom
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
tensorμ
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_tensorHom
Mathlib.Tactic.Monoidal.evalHorizontalComp_nil_nil
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_whiskerLeft
Mathlib.Tactic.Monoidal.evalWhiskerLeft_nil
Mathlib.Tactic.Monoidal.eval_whiskerRight
Mathlib.Tactic.Monoidal.evalWhiskerRight_nil
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_tensorHom
Mathlib.Tactic.Monoidal.naturality_leftUnitor
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_associator
Mathlib.Tactic.Monoidal.naturality_whiskerLeft
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_whiskerRight
Mathlib.Tactic.Monoidal.naturality_rightUnitor
CategoryTheory.braiding_leftUnitor
Mathlib.Tactic.Monoidal.eval_of
Mathlib.Tactic.Monoidal.evalComp_cons
Mathlib.Tactic.Monoidal.evalWhiskerRight_cons_of_of
Mathlib.Tactic.Monoidal.evalWhiskerRightAux_of
Mathlib.Tactic.Monoidal.evalComp_nil_cons
Mathlib.Tactic.Monoidal.evalWhiskerLeft_id
Mathlib.Tactic.BicategoryLike.mk_eq_of_cons
Mathlib.Tactic.Monoidal.naturality_id
leftUnitor_monoidal_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
tensorμ
CategoryTheory.MonoidalCategoryStruct.whiskerRight
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
leftUnitor_monoidal
rightUnitor_monoidal šŸ“–mathematical—CategoryTheory.MonoidalCategoryStruct.tensorHom
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
tensorμ
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategoryStruct.leftUnitor
—Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_tensorHom
Mathlib.Tactic.Monoidal.evalHorizontalComp_nil_nil
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_whiskerLeft
Mathlib.Tactic.Monoidal.evalWhiskerLeft_nil
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_tensorHom
Mathlib.Tactic.Monoidal.naturality_rightUnitor
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_associator
Mathlib.Tactic.Monoidal.naturality_whiskerLeft
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_leftUnitor
CategoryTheory.braiding_rightUnitor
Mathlib.Tactic.Monoidal.eval_of
Mathlib.Tactic.Monoidal.evalComp_cons
Mathlib.Tactic.Monoidal.evalWhiskerLeft_of_cons
Mathlib.Tactic.Monoidal.evalComp_nil_cons
Mathlib.Tactic.Monoidal.eval_whiskerRight
Mathlib.Tactic.Monoidal.evalWhiskerRight_id
Mathlib.Tactic.BicategoryLike.mk_eq_of_cons
Mathlib.Tactic.Monoidal.naturality_id
rightUnitor_monoidal_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
tensorμ
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategoryStruct.leftUnitor
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
rightUnitor_monoidal
tensor_associativity šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.BraidedCategory.braiding_tensor_left_hom
CategoryTheory.BraidedCategory.braiding_tensor_right_hom
Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_whiskerRight
Mathlib.Tactic.Monoidal.eval_whiskerLeft
Mathlib.Tactic.Monoidal.evalWhiskerLeft_nil
Mathlib.Tactic.Monoidal.eval_of
Mathlib.Tactic.Monoidal.evalWhiskerRight_cons_of_of
Mathlib.Tactic.Monoidal.evalWhiskerRight_nil
Mathlib.Tactic.Monoidal.evalWhiskerRightAux_of
Mathlib.Tactic.Monoidal.evalComp_cons
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.evalComp_nil_cons
Mathlib.Tactic.Monoidal.evalWhiskerLeft_of_cons
Mathlib.Tactic.Monoidal.evalWhiskerRight_cons_whisker
Mathlib.Tactic.Monoidal.evalWhiskerRight_comp
Mathlib.Tactic.Monoidal.evalWhiskerLeft_comp
Mathlib.Tactic.Monoidal.eval_tensorHom
Mathlib.Tactic.Monoidal.evalHorizontalComp_nil_nil
Mathlib.Tactic.Monoidal.eval_monoidalComp
Mathlib.Tactic.BicategoryLike.mk_eq_of_cons
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_whiskerRight
Mathlib.Tactic.Monoidal.naturality_associator
Mathlib.Tactic.Monoidal.naturality_whiskerLeft
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_id
Mathlib.Tactic.Monoidal.naturality_tensorHom
whisker_exchange
tensor_associativity_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
tensor_associativity
tensor_left_unitality šŸ“–mathematical—CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.inv
tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
—whiskerRight_tensor
leftUnitor_inv_whiskerRight
comp_whiskerRight
CategoryTheory.Category.assoc
pentagon_inv_inv_hom_hom_inv
id_whiskerLeft
CategoryTheory.Iso.inv_hom_id_assoc
whiskerLeft_comp
CategoryTheory.Iso.hom_inv_id_assoc
CategoryTheory.leftUnitor_inv_braiding
triangle_assoc_comp_right_inv_assoc
tensorHom_def
whiskerRight_id
leftUnitor_whiskerRight
triangle_assoc_comp_right_inv
triangle_assoc_comp_right_assoc
tensor_whiskerLeft
whiskerLeft_hom_inv
CategoryTheory.Category.comp_id
whiskerLeft_inv_hom
tensor_left_unitality_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.inv
tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
tensor_left_unitality
tensor_right_unitality šŸ“–mathematical—CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
—Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_whiskerLeft
Mathlib.Tactic.Monoidal.evalWhiskerLeft_nil
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.eval_whiskerRight
Mathlib.Tactic.Monoidal.evalWhiskerRight_nil
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_whiskerLeft
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_leftUnitor
Mathlib.Tactic.Monoidal.naturality_associator
Mathlib.Tactic.Monoidal.naturality_whiskerRight
Mathlib.Tactic.Monoidal.naturality_rightUnitor
CategoryTheory.Category.assoc
whiskerLeft_comp
comp_whiskerRight
CategoryTheory.rightUnitor_inv_braiding
whiskerRight_id
whiskerLeft_rightUnitor
whiskerLeft_rightUnitor_inv
pentagon_hom_hom_inv_inv_hom
CategoryTheory.Iso.inv_hom_id_assoc
triangle_assoc_comp_left_inv_assoc
tensorHom_def
whiskerRight_tensor
CategoryTheory.Iso.hom_inv_id_assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
inv_hom_whiskerRight
tensor_right_unitality_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.rightUnitor
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.leftUnitor
tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
tensor_right_unitality
tensor_Ī“ šŸ“–mathematical—CategoryTheory.Functor.OplaxMonoidal.Ī“
CategoryTheory.uniformProd
prodMonoidal
tensor
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
tensorMonoidal
tensorΓ
——
tensor_ε šŸ“–mathematical—CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.uniformProd
prodMonoidal
tensor
CategoryTheory.Functor.Monoidal.toLaxMonoidal
tensorMonoidal
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
——
tensor_Ī· šŸ“–mathematical—CategoryTheory.Functor.OplaxMonoidal.Ī·
CategoryTheory.uniformProd
prodMonoidal
tensor
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
tensorMonoidal
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
——
tensor_μ šŸ“–mathematical—CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.uniformProd
prodMonoidal
tensor
CategoryTheory.Functor.Monoidal.toLaxMonoidal
tensorMonoidal
tensorμ
——
tensorĪ“_tensorμ šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
tensorΓ
tensorμ
CategoryTheory.CategoryStruct.id
—CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.Iso.hom_inv_id_assoc
inv_hom_whiskerRight_assoc
CategoryTheory.Iso.inv_hom_id
whiskerLeft_id
CategoryTheory.Category.id_comp
CategoryTheory.Iso.hom_inv_id
tensorĪ“_tensorμ_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
tensorΓ
tensorμ
—CategoryTheory.Category.assoc
CategoryTheory.Category.id_comp
Mathlib.Tactic.Reassoc.eq_whisker'
tensorΓ_tensorμ
tensorμ_comp_μ_tensorHom_μ_comp_μ šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.Functor.obj
tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Functor.LaxBraided.toLaxMonoidal
CategoryTheory.Functor.map
—tensorHom_def
CategoryTheory.Category.assoc
CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ
associator_inv_naturality_left_assoc
pentagon_inv_assoc
comp_whiskerRight_assoc
CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ
whiskerLeft_hom_inv_assoc
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.Functor.LaxMonoidal.μ_natural_left_assoc
associator_inv_naturality_middle_assoc
whiskerLeft_comp
CategoryTheory.Functor.LaxBraided.braided
whiskerLeft_comp_assoc
CategoryTheory.Functor.LaxMonoidal.μ_natural_right
CategoryTheory.Functor.LaxMonoidal.whiskerLeft_μ_comp_μ_assoc
CategoryTheory.Iso.hom_inv_id_assoc
CategoryTheory.Functor.LaxMonoidal.μ_whiskerRight_comp_μ_assoc
tensorHom_def_assoc
whisker_assoc
pentagon_inv_inv_hom_hom_inv
pentagon_inv_hom_hom_hom_inv_assoc
tensorμ_comp_μ_tensorHom_μ_comp_μ_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.Functor.obj
tensorμ
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.Functor.LaxBraided.toLaxMonoidal
CategoryTheory.Functor.map
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
tensorμ_comp_μ_tensorHom_μ_comp_μ
tensorμ_natural šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensorμ
—CategoryTheory.Category.assoc
associator_naturality
tensorHom_comp_tensorHom
CategoryTheory.Category.comp_id
CategoryTheory.Category.id_comp
associator_inv_naturality
CategoryTheory.BraidedCategory.braiding_naturality
tensorμ_natural_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensorμ
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
tensorμ_natural
tensorμ_natural_left šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensorμ
—whiskerRight_tensor
CategoryTheory.Category.assoc
tensorHom_id
id_whiskerRight
tensorμ_natural
tensorμ_natural_left_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensorμ
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
tensorμ_natural_left
tensorμ_natural_right šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensorμ
—tensor_whiskerLeft
CategoryTheory.Category.assoc
tensorHom_id
id_whiskerRight
id_tensorHom
tensorμ_natural
tensorμ_natural_right_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.MonoidalCategoryStruct.tensorHom
tensorμ
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
tensorμ_natural_right
tensorμ_tensorĪ“ šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
tensorμ
tensorΓ
CategoryTheory.CategoryStruct.id
—CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.Iso.hom_inv_id_assoc
hom_inv_whiskerRight_assoc
CategoryTheory.Iso.inv_hom_id
whiskerLeft_id
CategoryTheory.Category.id_comp
CategoryTheory.Iso.hom_inv_id
tensorμ_tensorĪ“_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
toMonoidalCategoryStruct
tensorμ
tensorΓ
—CategoryTheory.Category.assoc
CategoryTheory.Category.id_comp
Mathlib.Tactic.Reassoc.eq_whisker'
tensorμ_tensorΓ

CategoryTheory.MonoidalOpposite

Definitions

NameCategoryTheorems
instBraidedMopFunctor šŸ“–CompOp—
instBraidedUnmopFunctor šŸ“–CompOp—
instBraiding šŸ“–CompOp
8 mathmath: unmop_hom_braiding, mop_inv_braiding, mopFunctor_μ, mop_hom_braiding, unmop_inv_braiding, mop_braiding, mopFunctor_Γ, unmop_braiding
instMonoidalMopFunctor šŸ“–CompOp
4 mathmath: mopFunctor_ε, mopFunctor_η, mopFunctor_μ, mopFunctor_Γ
instMonoidalUnmopFunctor šŸ“–CompOp
4 mathmath: unmopFunctor_Γ, unmopFunctor_μ, unmopFunctor_η, unmopFunctor_ε

Theorems

NameKindAssumesProvesValidatesDepends On
mopFunctor_Ī“ šŸ“–mathematical—CategoryTheory.Functor.OplaxMonoidal.Ī“
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
CategoryTheory.mopFunctor
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
instMonoidalMopFunctor
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
mop
CategoryTheory.BraidedCategory.braiding
instBraiding
——
mopFunctor_ε šŸ“–mathematical—CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
CategoryTheory.mopFunctor
CategoryTheory.Functor.Monoidal.toLaxMonoidal
instMonoidalMopFunctor
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
——
mopFunctor_Ī· šŸ“–mathematical—CategoryTheory.Functor.OplaxMonoidal.Ī·
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
CategoryTheory.mopFunctor
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
instMonoidalMopFunctor
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
——
mopFunctor_μ šŸ“–mathematical—CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
CategoryTheory.mopFunctor
CategoryTheory.Functor.Monoidal.toLaxMonoidal
instMonoidalMopFunctor
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
mop
CategoryTheory.BraidedCategory.braiding
instBraiding
——
mop_braiding šŸ“–mathematical—CategoryTheory.Iso.mop
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
instBraiding
mop
——
mop_hom_braiding šŸ“–mathematical—Quiver.Hom.mop
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
mop
instBraiding
——
mop_inv_braiding šŸ“–mathematical—Quiver.Hom.mop
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.inv
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
mop
instBraiding
——
unmopFunctor_Ī“ šŸ“–mathematical—CategoryTheory.Functor.OplaxMonoidal.Ī“
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
CategoryTheory.unmopFunctor
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
instMonoidalUnmopFunctor
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
unmop
CategoryTheory.BraidedCategory.braiding
——
unmopFunctor_ε šŸ“–mathematical—CategoryTheory.Functor.LaxMonoidal.ε
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
CategoryTheory.unmopFunctor
CategoryTheory.Functor.Monoidal.toLaxMonoidal
instMonoidalUnmopFunctor
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
——
unmopFunctor_Ī· šŸ“–mathematical—CategoryTheory.Functor.OplaxMonoidal.Ī·
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
CategoryTheory.unmopFunctor
CategoryTheory.Functor.Monoidal.toOplaxMonoidal
instMonoidalUnmopFunctor
CategoryTheory.CategoryStruct.id
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
——
unmopFunctor_μ šŸ“–mathematical—CategoryTheory.Functor.LaxMonoidal.μ
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.monoidalCategoryMop
CategoryTheory.unmopFunctor
CategoryTheory.Functor.Monoidal.toLaxMonoidal
instMonoidalUnmopFunctor
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
unmop
CategoryTheory.BraidedCategory.braiding
——
unmop_braiding šŸ“–mathematical—CategoryTheory.Iso.unmop
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.monoidalCategoryMop
CategoryTheory.BraidedCategory.braiding
instBraiding
unmop
——
unmop_hom_braiding šŸ“–mathematical—Quiver.Hom.unmop
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.monoidalCategoryMop
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
instBraiding
unmop
——
unmop_inv_braiding šŸ“–mathematical—Quiver.Hom.unmop
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalOpposite
monoidalOppositeCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.monoidalCategoryMop
CategoryTheory.Iso.inv
CategoryTheory.BraidedCategory.braiding
instBraiding
unmop
——

CategoryTheory.SymmetricCategory

Definitions

NameCategoryTheorems
equivReverseBraiding šŸ“–CompOp—
ofFaithful šŸ“–CompOp—
ofFullyFaithful šŸ“–CompOp—
toBraidedCategory šŸ“–CompOp
24 mathmath: CategoryTheory.MonObj.instIsMonHomHomBraiding, CategoryTheory.GradedObject.Monoidal.symmetry, CategoryTheory.symmetricOfHasFiniteProducts_braiding_hom, CategoryTheory.CopyDiscardCategory.copy_tensor, CategoryTheory.coprodComparison_tensorRight_braiding_hom, CategoryTheory.GradedObject.Monoidal.symmetry_assoc, CategoryTheory.symmetricOfHasFiniteCoproducts_braiding, reverseBraiding_eq, SemimoduleCat.MonoidalCategory.tensorμ_apply, braiding_swap_eq_inv_braiding, SemimoduleCat.MonoidalCategory.braiding_hom_apply, SemimoduleCat.MonoidalCategory.braiding_inv_apply, CategoryTheory.MonoidalCategory.DayConvolution.symmetry, CategoryTheory.Mon.instIsCommMonObj, symmetry_assoc, symmetry, rightDistrib_of_leftDistrib, SemimoduleCat.MonoidalCategory.tensorμ_eq_tensorTensorTensorComm, CategoryTheory.MonObj.mul_braiding, CategoryTheory.instIsCommMonObjTensorObj, CategoryTheory.Mon.braiding_inv_hom, CategoryTheory.symmetricOfHasFiniteProducts_braiding_inv, CategoryTheory.CopyDiscardCategory.isCommComonObj, CategoryTheory.Mon.braiding_hom_hom

Theorems

NameKindAssumesProvesValidatesDepends On
braiding_swap_eq_inv_braiding šŸ“–mathematical—CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.BraidedCategory.braiding
toBraidedCategory
CategoryTheory.Iso.inv
—CategoryTheory.Iso.inv_ext'
symmetry
reverseBraiding_eq šŸ“–mathematical—CategoryTheory.reverseBraiding
toBraidedCategory
—CategoryTheory.Iso.ext
braiding_swap_eq_inv_braiding
symmetry šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
toBraidedCategory
CategoryTheory.CategoryStruct.id
——
symmetry_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
toBraidedCategory
—CategoryTheory.Category.assoc
CategoryTheory.Category.id_comp
Mathlib.Tactic.Reassoc.eq_whisker'
symmetry

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