Documentation Verification Report

Hopf_

šŸ“ Source: Mathlib/CategoryTheory/Monoidal/Hopf_.lean

Statistics

MetricCount
DefinitionsHopf, X, hopf, instCategory, toBimon, toBimon_, HopfObj, antipode, termš’®, toBimonObj, Ā«termš’®[_]Ā», Hopf_, Hopf_Class
13
Theoremsantipode_antipode, antipode_comul, antipode_comul₁, antipode_comulā‚‚, antipode_counit, antipode_counit_assoc, antipode_left, antipode_left_assoc, antipode_right, antipode_right_assoc, hom_antipode, mul_antipode, mul_antipode₁, mul_antipodeā‚‚, one_antipode, one_antipode_assoc
16
Total29

CategoryTheory

Definitions

NameCategoryTheorems
Hopf šŸ“–CompData—
HopfObj šŸ“–CompData—
Hopf_ šŸ“–CompOp—
Hopf_Class šŸ“–CompOp—

CategoryTheory.Hopf

Definitions

NameCategoryTheorems
X šŸ“–CompOp—
hopf šŸ“–CompOp—
instCategory šŸ“–CompOp—
toBimon šŸ“–CompOp—
toBimon_ šŸ“–CompOp—

CategoryTheory.HopfObj

Definitions

NameCategoryTheorems
antipode šŸ“–CompOp
16 mathmath: mul_antipode, one_antipode, antipode_left, antipode_comul, antipode_comulā‚‚, antipode_left_assoc, mul_antipode₁, antipode_right_assoc, antipode_comul₁, antipode_antipode, mul_antipodeā‚‚, antipode_counit, antipode_right, antipode_counit_assoc, one_antipode_assoc, hom_antipode
termš’® šŸ“–CompOp—
toBimonObj šŸ“–CompOp
14 mathmath: mul_antipode, one_antipode, antipode_left, antipode_comul, antipode_comulā‚‚, antipode_left_assoc, mul_antipode₁, antipode_right_assoc, antipode_comul₁, mul_antipodeā‚‚, antipode_counit, antipode_right, antipode_counit_assoc, one_antipode_assoc
Ā«termš’®[_]Ā» šŸ“–CompOp—

Theorems

NameKindAssumesProvesValidatesDepends On
antipode_antipode šŸ“–mathematicalCategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonObj.mul
CategoryTheory.BimonObj.toMonObj
toBimonObj
antipode
CategoryTheory.CategoryStruct.id
—left_inv_eq_right_inv
CategoryTheory.Conv.mul_eq
CategoryTheory.Conv.one_eq
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensorHom_def_assoc
mul_antipode
antipode_left_assoc
one_antipode
CategoryTheory.MonoidalCategory.whiskerLeft_id
CategoryTheory.Category.id_comp
antipode_left
antipode_comul šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
antipode
CategoryTheory.ComonObj.comul
CategoryTheory.BimonObj.toComonObj
toBimonObj
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonoidalCategoryStruct.tensorHom
—left_inv_eq_right_inv
CategoryTheory.Conv.mul_eq
CategoryTheory.Conv.one_eq
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.MonoidalCategory.tensor_whiskerLeft
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id_assoc
antipode_comul₁
CategoryTheory.MonoidalCategory.whiskerLeft_comp
antipode_comulā‚‚
antipode_comul₁ šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.ComonObj.comul
CategoryTheory.BimonObj.toComonObj
toBimonObj
CategoryTheory.MonoidalCategoryStruct.whiskerRight
antipode
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.MonObj.mul
CategoryTheory.BimonObj.toMonObj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.ComonObj.counit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonObj.one
—CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.associator_naturality_right
CategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.Bimon.compatibility
antipode_left
CategoryTheory.BimonObj.one_comul
antipode_comulā‚‚ šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.ComonObj.comul
CategoryTheory.BimonObj.toComonObj
toBimonObj
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonoidalCategoryStruct.tensorHom
antipode
CategoryTheory.Iso.inv
CategoryTheory.MonObj.mul
CategoryTheory.BimonObj.toMonObj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.ComonObj.counit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonObj.one
—CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.MonoidalCategory.whiskerLeft_comp
CategoryTheory.MonoidalCategory.associator_inv_naturality_middle
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.BraidedCategory.braiding_naturality_right
CategoryTheory.MonoidalCategory.associator_naturality_left
CategoryTheory.BraidedCategory.braiding_naturality_left
CategoryTheory.MonoidalCategory.associator_inv_naturality_right
CategoryTheory.MonoidalCategory.whisker_exchange
CategoryTheory.BraidedCategory.hexagon_reverse_assoc
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.ComonObj.comul_assoc_flip_assoc
CategoryTheory.ComonObj.comul_assoc
CategoryTheory.MonoidalCategory.associator_naturality_middle_assoc
CategoryTheory.Iso.hom_inv_id_assoc
antipode_right
CategoryTheory.ComonObj.counit_comul
CategoryTheory.MonoidalCategory.associator_inv_naturality_right_assoc
CategoryTheory.braiding_tensorUnit_left
CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor_inv
CategoryTheory.MonoidalCategory.whiskerRight_id
CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor
CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom_assoc
antipode_right_assoc
CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality_assoc
CategoryTheory.MonoidalCategory.tensorHom_def
Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_of
Mathlib.Tactic.Monoidal.eval_whiskerRight
Mathlib.Tactic.Monoidal.evalWhiskerRight_id
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_id
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_inv
Mathlib.Tactic.Monoidal.naturality_rightUnitor
Mathlib.Tactic.Monoidal.naturality_leftUnitor
Mathlib.Tactic.Monoidal.naturality_whiskerLeft
antipode_counit šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
antipode
CategoryTheory.ComonObj.counit
CategoryTheory.BimonObj.toComonObj
toBimonObj
—CategoryTheory.MonoidalCategory.whiskerRight_id
CategoryTheory.MonoidalCategory.unitors_equal
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.ComonObj.comul_counit_assoc
CategoryTheory.BimonObj.one_counit
CategoryTheory.MonoidalCategory.whisker_exchange_assoc
CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.Bimon.mul_counit
antipode_left_assoc
antipode_counit_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
antipode
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.ComonObj.counit
CategoryTheory.BimonObj.toComonObj
toBimonObj
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
antipode_counit
antipode_left šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.ComonObj.comul
CategoryTheory.BimonObj.toComonObj
toBimonObj
CategoryTheory.MonoidalCategoryStruct.whiskerRight
antipode
CategoryTheory.MonObj.mul
CategoryTheory.BimonObj.toMonObj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.ComonObj.counit
CategoryTheory.MonObj.one
——
antipode_left_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.ComonObj.comul
CategoryTheory.BimonObj.toComonObj
toBimonObj
CategoryTheory.MonoidalCategoryStruct.whiskerRight
antipode
CategoryTheory.MonObj.mul
CategoryTheory.BimonObj.toMonObj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.ComonObj.counit
CategoryTheory.MonObj.one
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
antipode_left
antipode_right šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.ComonObj.comul
CategoryTheory.BimonObj.toComonObj
toBimonObj
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
antipode
CategoryTheory.MonObj.mul
CategoryTheory.BimonObj.toMonObj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.ComonObj.counit
CategoryTheory.MonObj.one
——
antipode_right_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.ComonObj.comul
CategoryTheory.BimonObj.toComonObj
toBimonObj
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
antipode
CategoryTheory.MonObj.mul
CategoryTheory.BimonObj.toMonObj
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.ComonObj.counit
CategoryTheory.MonObj.one
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
antipode_right
hom_antipode šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
antipode
—left_inv_eq_right_inv
CategoryTheory.Conv.mul_eq
CategoryTheory.Conv.one_eq
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.whisker_exchange
CategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.IsComonHom.hom_comul
CategoryTheory.IsBimonHom.toIsComonHom
antipode_left
CategoryTheory.IsComonHom.hom_counit
CategoryTheory.MonoidalCategory.whiskerLeft_comp
CategoryTheory.IsMonHom.mul_hom
CategoryTheory.IsBimonHom.toIsMonHom
antipode_right
CategoryTheory.IsMonHom.one_hom
mul_antipode šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonObj.mul
CategoryTheory.BimonObj.toMonObj
toBimonObj
antipode
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.Iso.hom
CategoryTheory.BraidedCategory.braiding
—left_inv_eq_right_inv
CategoryTheory.Conv.mul_eq
CategoryTheory.Conv.one_eq
CategoryTheory.Comon.tensorObj_comul
CategoryTheory.MonoidalCategory.whiskerRight_tensor
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.pentagon_hom_inv_inv_inv_inv_assoc
mul_antipode₁
CategoryTheory.BraidedCategory.braiding_naturality_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_comp
mul_antipodeā‚‚
mul_antipode₁ šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.ComonObj.comul
CategoryTheory.BimonObj.toComonObj
toBimonObj
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonObj.mul
CategoryTheory.BimonObj.toMonObj
antipode
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.ComonObj.counit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonObj.one
—CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.associator_naturality_left
CategoryTheory.MonoidalCategory.whisker_exchange
CategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv_assoc
CategoryTheory.Bimon.compatibility_assoc
antipode_left
CategoryTheory.BimonObj.mul_counit_assoc
mul_antipodeā‚‚ šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorHom
CategoryTheory.ComonObj.comul
CategoryTheory.BimonObj.toComonObj
toBimonObj
CategoryTheory.Iso.hom
CategoryTheory.MonoidalCategoryStruct.associator
CategoryTheory.MonoidalCategoryStruct.whiskerLeft
CategoryTheory.Iso.inv
CategoryTheory.MonoidalCategoryStruct.whiskerRight
CategoryTheory.BraidedCategory.braiding
CategoryTheory.MonObj.mul
CategoryTheory.BimonObj.toMonObj
antipode
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.ComonObj.counit
CategoryTheory.MonoidalCategoryStruct.leftUnitor
CategoryTheory.MonObj.one
—CategoryTheory.Category.assoc
CategoryTheory.MonoidalCategory.associator_naturality_left
CategoryTheory.MonoidalCategory.whisker_exchange
CategoryTheory.MonObj.mul_assoc_flip
CategoryTheory.MonoidalCategory.associator_inv_naturality_left
CategoryTheory.MonObj.mul_assoc
CategoryTheory.MonoidalCategory.comp_whiskerRight
CategoryTheory.MonoidalCategory.tensorHom_def
CategoryTheory.MonoidalCategory.tensor_whiskerLeft
CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_hom_inv_assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.id_comp
CategoryTheory.BraidedCategory.hexagon_forward
CategoryTheory.MonoidalCategory.whiskerLeft_comp
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.MonoidalCategory.pentagon_inv_inv_hom_inv_inv
CategoryTheory.MonoidalCategory.whisker_assoc
CategoryTheory.MonoidalCategory.whiskerLeft_inv_hom_assoc
CategoryTheory.BraidedCategory.braiding_naturality_right
CategoryTheory.MonoidalCategory.tensorHom_def'
CategoryTheory.MonoidalCategory.associator_naturality_right
CategoryTheory.MonoidalCategory.associator_inv_naturality_middle_assoc
CategoryTheory.Iso.hom_inv_id_assoc
antipode_right
CategoryTheory.MonObj.one_mul
CategoryTheory.BraidedCategory.braiding_naturality_left
CategoryTheory.MonoidalCategory.associator_naturality_middle_assoc
CategoryTheory.braiding_tensorUnit_right
CategoryTheory.MonoidalCategory.whiskerLeft_id
CategoryTheory.MonoidalCategory.whiskerLeft_rightUnitor
CategoryTheory.MonoidalCategory.rightUnitor_naturality
CategoryTheory.MonoidalCategory.associator_inv_naturality_right_assoc
Mathlib.Tactic.BicategoryLike.mk_eq
Mathlib.Tactic.Monoidal.eval_comp
Mathlib.Tactic.Monoidal.eval_tensorHom
Mathlib.Tactic.Monoidal.eval_of
Mathlib.Tactic.Monoidal.evalHorizontalComp_cons_cons
Mathlib.Tactic.Monoidal.evalHorizontalCompAux_of
Mathlib.Tactic.Monoidal.evalHorizontalComp_nil_nil
Mathlib.Tactic.Monoidal.evalComp_cons
Mathlib.Tactic.Monoidal.evalComp_nil_nil
Mathlib.Tactic.Monoidal.evalComp_nil_cons
Mathlib.Tactic.BicategoryLike.mk_eq_of_cons
Mathlib.Tactic.Monoidal.mk_eq_of_naturality
Mathlib.Tactic.Monoidal.naturality_comp
Mathlib.Tactic.Monoidal.naturality_tensorHom
Mathlib.Tactic.Monoidal.naturality_id
Mathlib.Tactic.Monoidal.naturality_rightUnitor
Mathlib.Tactic.Monoidal.naturality_leftUnitor
one_antipode šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonObj.one
CategoryTheory.BimonObj.toMonObj
toBimonObj
antipode
—CategoryTheory.MonoidalCategory.whiskerRight_id
CategoryTheory.MonObj.mul_one
CategoryTheory.Category.assoc
CategoryTheory.Iso.inv_hom_id
CategoryTheory.Category.comp_id
CategoryTheory.Iso.inv_hom_id_assoc
CategoryTheory.BimonObj.one_counit_assoc
CategoryTheory.MonoidalCategory.rightUnitor_inv_naturality_assoc
CategoryTheory.MonoidalCategory.whisker_exchange_assoc
CategoryTheory.MonoidalCategory.unitors_inv_equal
CategoryTheory.MonoidalCategory.tensorHom_def_assoc
CategoryTheory.Bimon.one_comul_assoc
antipode_left
one_antipode_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.MonObj.one
CategoryTheory.BimonObj.toMonObj
toBimonObj
antipode
—CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
one_antipode

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