Documentation Verification Report

Mon_

πŸ“ Source: Mathlib/CategoryTheory/Monoidal/Cartesian/Mon_.lean

Statistics

MetricCount
DefinitionsinstAddMonObjOfIsCommAddMonObjX, instCartesianMonoidalCategory, uniqueHomToTrivial, ofRepresentableBy, homAddEquiv, homMulEquiv, homAddMonoidHom, homMonoidHom, addCommMonoid, addEquivCongrRight, addMonoid, commMonoid, monoid, mulEquivCongrRight, instCartesianMonoidalCategory, instMonObjOfIsCommMonObjX, uniqueHomToTrivial, ofRepresentableBy, instHasZeroMorphismsAddMon, instHasZeroMorphismsMon, uniqueHomToTrivial, yonedaAddMon, yonedaAddMonFullyFaithful, yonedaAddMonObj, yonedaAddMonObjIsoOfRepresentableBy, yonedaAddMonObjRepresentableBy, yonedaMon, yonedaMonFullyFaithful, yonedaMonObj, yonedaMonObjIsoOfRepresentableBy, yonedaMonObjRepresentableBy
31
Theoremshom_add, hom_nsmul, hom_zero, fst_hom, hom_add, hom_zero, instIsCommAddMonObj, lift_hom, snd_hom, uniqueHomToTrivial_default_hom, add_comp, add_comp_assoc, add_eq_add, comp_add, comp_add_assoc, comp_nsmul, comp_nsmul_assoc, comp_zero, comp_zero_assoc, instIsAddMonHomAddOfIsCommAddMonObj, instIsAddMonHomFst, instIsAddMonHomLift, instIsAddMonHomSnd, instIsAddMonHomToAddUnit, instIsAddMonHomZero, lift_comp_zero_left, lift_comp_zero_left_assoc, lift_comp_zero_right, lift_comp_zero_right_assoc, lift_lift_assoc, nsmul_comp, nsmul_comp_assoc, ofRepresentableBy_add, ofRepresentableBy_yonedaAddMonObjRepresentableBy, ofRepresentableBy_zero, zero_comp, zero_comp_assoc, zero_eq_zero, homAddEquiv_apply, homAddEquiv_symm_apply, homMulEquiv_apply, homMulEquiv_symm_apply, homAddMonoidHom_apply, homMonoidHom_apply, map_add', map_mul, map_one, map_zero', addEquivCongrRight_apply, addEquivCongrRight_symm_apply, add_def, mulEquivCongrRight_apply, mulEquivCongrRight_symm_apply, mul_def, one_def, zero_def, hom_mul, hom_one, hom_pow, fst_hom, hom_mul, hom_one, instIsCommMonObj, lift_hom, snd_hom, uniqueHomToTrivial_default_hom, comp_mul, comp_mul_assoc, comp_one, comp_one_assoc, comp_pow, comp_pow_assoc, instIsMonHomFst, instIsMonHomLift, instIsMonHomMulOfIsCommMonObj, instIsMonHomOne, instIsMonHomSnd, instIsMonHomToUnit, lift_comp_one_left, lift_comp_one_left_assoc, lift_comp_one_right, lift_comp_one_right_assoc, lift_lift_assoc, mul_comp, mul_comp_assoc, mul_eq_mul, ofRepresentableBy_mul, ofRepresentableBy_one, ofRepresentableBy_yonedaMonObjRepresentableBy, one_comp, one_comp_assoc, one_eq_one, pow_comp, pow_comp_assoc, essImage_yonedaAddMon, essImage_yonedaMon, instFaithfulMonFunctorOppositeMonCatYonedaMon, instFaithfulMonFunctorOppositeMonCatyonedaAddMon, instFullMonFunctorOppositeMonCatYonedaMon, instFullMonFunctorOppositeMonCatyonedaAddMon, instHasZeroObjectAddMon, instHasZeroObjectMon, isCommAddMonObj_iff_isAddCommutative, isCommMonObj_iff_isMulCommutative, yonedaAddMonObjIsoOfRepresentableBy_hom_app_hom_apply, yonedaAddMonObjIsoOfRepresentableBy_inv_app_hom_apply, yonedaAddMonObj_map, yonedaAddMonObj_obj_coe, yonedaAddMon_map_app, yonedaAddMon_naturality, yonedaAddMon_naturality_assoc, yonedaAddMon_obj, yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, yonedaMonObj_map, yonedaMonObj_obj_coe, yonedaMon_map_app, yonedaMon_naturality, yonedaMon_naturality_assoc, yonedaMon_obj
120
Total151

CategoryTheory

Definitions

NameCategoryTheorems
instHasZeroMorphismsAddMon πŸ“–CompOpβ€”
instHasZeroMorphismsMon πŸ“–CompOpβ€”
uniqueHomToTrivial πŸ“–CompOpβ€”
yonedaAddMon πŸ“–CompOp
7 mathmath: yonedaAddMon_obj, instFullMonFunctorOppositeMonCatyonedaAddMon, Hom.addEquivCongrRight_symm_apply, instFaithfulMonFunctorOppositeMonCatyonedaAddMon, Hom.addEquivCongrRight_apply, essImage_yonedaAddMon, yonedaAddMon_map_app
yonedaAddMonFullyFaithful πŸ“–CompOpβ€”
yonedaAddMonObj πŸ“–CompOp
11 mathmath: yonedaAddMonObjIsoOfRepresentableBy_hom_app_hom_apply, yonedaAddMon_obj, yonedaAddMonObjIsoOfRepresentableBy_inv_app_hom_apply, Hom.addEquivCongrRight_symm_apply, yonedaAddMonObj_map, Hom.addEquivCongrRight_apply, yonedaAddMon_naturality_assoc, yonedaAddMonObj_obj_coe, yonedaAddMon_naturality, AddMonObj.ofRepresentableBy_yonedaAddMonObjRepresentableBy, yonedaAddMon_map_app
yonedaAddMonObjIsoOfRepresentableBy πŸ“–CompOp
2 mathmath: yonedaAddMonObjIsoOfRepresentableBy_hom_app_hom_apply, yonedaAddMonObjIsoOfRepresentableBy_inv_app_hom_apply
yonedaAddMonObjRepresentableBy πŸ“–CompOp
1 mathmath: AddMonObj.ofRepresentableBy_yonedaAddMonObjRepresentableBy
yonedaMon πŸ“–CompOp
11 mathmath: instFullMonFunctorOppositeMonCatYonedaMon, shrinkYonedaMon_map, essImage_yonedaMon, instFaithfulMonFunctorOppositeMonCatYonedaMon, shrinkYonedaMon_obj, yonedaMon_map_app, Hom.mulEquivCongrRight_symm_apply, instSmallCarrierObjOppositeMonCatMonFunctorYonedaMon, yonedaGrp_map_app, Hom.mulEquivCongrRight_apply, yonedaMon_obj
yonedaMonFullyFaithful πŸ“–CompOpβ€”
yonedaMonObj πŸ“–CompOp
12 mathmath: yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, yonedaMon_naturality_assoc, yonedaMonObj_map, yonedaMon_naturality, yonedaMonObj_obj_coe, yonedaMon_map_app, Hom.mulEquivCongrRight_symm_apply, yonedaGrpObj_map, MonObj.ofRepresentableBy_yonedaMonObjRepresentableBy, Hom.mulEquivCongrRight_apply, yonedaMon_obj
yonedaMonObjIsoOfRepresentableBy πŸ“–CompOp
2 mathmath: yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply
yonedaMonObjRepresentableBy πŸ“–CompOp
1 mathmath: MonObj.ofRepresentableBy_yonedaMonObjRepresentableBy

Theorems

NameKindAssumesProvesValidatesDepends On
essImage_yonedaAddMon πŸ“–mathematicalβ€”Functor.essImage
AddMon
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Functor
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
AddMon.instCategory
Functor.category
yonedaAddMon
Functor.IsRepresentable
Functor.comp
types
forget
AddMonoidHom
AddMonCat.carrier
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonCat.str
AddMonoidHom.instFunLike
AddMonCat.instConcreteCategoryAddMonoidHomCarrier
β€”β€”
essImage_yonedaMon πŸ“–mathematicalβ€”Functor.essImage
Mon
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Functor
Opposite
Category.opposite
MonCat
MonCat.instCategory
Mon.instCategory
Functor.category
yonedaMon
Functor.IsRepresentable
Functor.comp
types
forget
MonoidHom
MonCat.carrier
MulOneClass.toMulOne
Monoid.toMulOneClass
MonCat.str
MonoidHom.instFunLike
MonCat.instConcreteCategoryMonoidHomCarrier
β€”β€”
instFaithfulMonFunctorOppositeMonCatYonedaMon πŸ“–mathematicalβ€”Functor.Faithful
Mon
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Mon.instCategory
Functor
Opposite
Category.opposite
MonCat
MonCat.instCategory
Functor.category
yonedaMon
β€”Functor.FullyFaithful.faithful
instFaithfulMonFunctorOppositeMonCatyonedaAddMon πŸ“–mathematicalβ€”Functor.Faithful
AddMon
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
AddMon.instCategory
Functor
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
Functor.category
yonedaAddMon
β€”Functor.FullyFaithful.faithful
instFullMonFunctorOppositeMonCatYonedaMon πŸ“–mathematicalβ€”Functor.Full
Mon
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Mon.instCategory
Functor
Opposite
Category.opposite
MonCat
MonCat.instCategory
Functor.category
yonedaMon
β€”Functor.FullyFaithful.full
instFullMonFunctorOppositeMonCatyonedaAddMon πŸ“–mathematicalβ€”Functor.Full
AddMon
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
AddMon.instCategory
Functor
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
Functor.category
yonedaAddMon
β€”Functor.FullyFaithful.full
instHasZeroObjectAddMon πŸ“–mathematicalβ€”Limits.HasZeroObject
AddMon
SemiCartesianMonoidalCategory.toMonoidalCategory
AddMon.instCategory
β€”nonempty_unique
Unique.instSubsingleton
instHasZeroObjectMon πŸ“–mathematicalβ€”Limits.HasZeroObject
Mon
SemiCartesianMonoidalCategory.toMonoidalCategory
Mon.instCategory
β€”nonempty_unique
Unique.instSubsingleton
isCommAddMonObj_iff_isAddCommutative πŸ“–mathematicalβ€”IsCommAddMonObj
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
IsAddCommutative
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
Hom.addMonoid
β€”add_comm
AddMonObj.add_eq_add
AddMonObj.comp_add
CartesianMonoidalCategory.braiding_hom_fst
CartesianMonoidalCategory.braiding_hom_snd
isCommMonObj_iff_isMulCommutative πŸ“–mathematicalβ€”IsCommMonObj
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
IsMulCommutative
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Hom.monoid
β€”mul_comm
MonObj.mul_eq_mul
MonObj.comp_mul
CartesianMonoidalCategory.braiding_hom_fst
CartesianMonoidalCategory.braiding_hom_snd
yonedaAddMonObjIsoOfRepresentableBy_hom_app_hom_apply πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
Opposite.unop
AddMonCat.carrier
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
Hom.addMonoid
AddMonObj.ofRepresentableBy
AddMonCat.str
AddMonoidHom.instFunLike
AddMonCat.Hom.hom'
Functor.obj
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
yonedaAddMonObj
NatTrans.app
Iso.hom
Functor
Functor.category
yonedaAddMonObjIsoOfRepresentableBy
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Functor.RepresentableBy.homEquiv
Functor.comp
types
forget
AddMonCat.instConcreteCategoryAddMonoidHomCarrier
β€”β€”
yonedaAddMonObjIsoOfRepresentableBy_inv_app_hom_apply πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
AddMonCat.carrier
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
Opposite.unop
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonCat.str
Hom.addMonoid
AddMonObj.ofRepresentableBy
AddMonoidHom.instFunLike
AddMonCat.Hom.hom'
Functor.obj
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
yonedaAddMonObj
NatTrans.app
Iso.inv
Functor
Functor.category
yonedaAddMonObjIsoOfRepresentableBy
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
Functor.RepresentableBy.homEquiv
Functor.comp
types
forget
AddMonCat.instConcreteCategoryAddMonoidHomCarrier
β€”β€”
yonedaAddMonObj_map πŸ“–mathematicalβ€”Functor.map
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
yonedaAddMonObj
AddMonCat.ofHom
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
Opposite.unop
Hom.addMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddZero.toZero
CategoryStruct.comp
Quiver.Hom.unop
β€”β€”
yonedaAddMonObj_obj_coe πŸ“–mathematicalβ€”AddMonCat.carrier
Functor.obj
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
yonedaAddMonObj
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
Opposite.unop
β€”β€”
yonedaAddMon_map_app πŸ“–mathematicalβ€”NatTrans.app
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
yonedaAddMonObj
AddMon.X
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
AddMon.addMon
Functor.map
AddMon
AddMon.instCategory
Functor
Functor.category
yonedaAddMon
AddMonCat.ofHom
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
Opposite.unop
Hom.addMonoid
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddZero.toZero
CategoryStruct.comp
AddMon.Hom.hom
β€”β€”
yonedaAddMon_naturality πŸ“–mathematicalβ€”DFunLike.coe
Functor.obj
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
yonedaAddMonObj
Opposite.op
AddMonCat.carrier
ConcreteCategory.hom
AddMonoidHom
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonCat.str
AddMonoidHom.instFunLike
AddMonCat.instConcreteCategoryAddMonoidHomCarrier
NatTrans.app
CategoryStruct.comp
Category.toCategoryStruct
Opposite.unop
β€”NatTrans.naturality
yonedaAddMon_naturality_assoc πŸ“–mathematicalβ€”CategoryStruct.comp
Category.toCategoryStruct
DFunLike.coe
AddMonoidHom
AddMonCat.carrier
Functor.obj
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
yonedaAddMonObj
Opposite.op
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonCat.str
ConcreteCategory.hom
AddMonoidHom.instFunLike
AddMonCat.instConcreteCategoryAddMonoidHomCarrier
NatTrans.app
β€”Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
yonedaAddMon_naturality
yonedaAddMon_obj πŸ“–mathematicalβ€”Functor.obj
AddMon
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
AddMon.instCategory
Functor
Opposite
Category.opposite
AddMonCat
AddMonCat.instCategory
Functor.category
yonedaAddMon
yonedaAddMonObj
AddMon.X
AddMon.addMon
β€”β€”
yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
Opposite.unop
MonCat.carrier
MulOneClass.toMulOne
Monoid.toMulOneClass
Hom.monoid
MonObj.ofRepresentableBy
MonCat.str
MonoidHom.instFunLike
MonCat.Hom.hom
Functor.obj
Opposite
Category.opposite
MonCat
MonCat.instCategory
yonedaMonObj
NatTrans.app
Iso.hom
Functor
Functor.category
yonedaMonObjIsoOfRepresentableBy
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Functor.RepresentableBy.homEquiv
Functor.comp
types
forget
MonCat.instConcreteCategoryMonoidHomCarrier
β€”β€”
yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
MonCat.carrier
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
Opposite.unop
MulOneClass.toMulOne
Monoid.toMulOneClass
MonCat.str
Hom.monoid
MonObj.ofRepresentableBy
MonoidHom.instFunLike
MonCat.Hom.hom
Functor.obj
Opposite
Category.opposite
MonCat
MonCat.instCategory
yonedaMonObj
NatTrans.app
Iso.inv
Functor
Functor.category
yonedaMonObjIsoOfRepresentableBy
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
Functor.RepresentableBy.homEquiv
Functor.comp
types
forget
MonCat.instConcreteCategoryMonoidHomCarrier
β€”β€”
yonedaMonObj_map πŸ“–mathematicalβ€”Functor.map
Opposite
Category.opposite
MonCat
MonCat.instCategory
yonedaMonObj
MonCat.ofHom
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
Opposite.unop
Hom.monoid
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
CategoryStruct.comp
Quiver.Hom.unop
β€”β€”
yonedaMonObj_obj_coe πŸ“–mathematicalβ€”MonCat.carrier
Functor.obj
Opposite
Category.opposite
MonCat
MonCat.instCategory
yonedaMonObj
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
Opposite.unop
β€”β€”
yonedaMon_map_app πŸ“–mathematicalβ€”NatTrans.app
Opposite
Category.opposite
MonCat
MonCat.instCategory
yonedaMonObj
Mon.X
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Mon.mon
Functor.map
Mon
Mon.instCategory
Functor
Functor.category
yonedaMon
MonCat.ofHom
Quiver.Hom
CategoryStruct.toQuiver
Category.toCategoryStruct
Opposite.unop
Hom.monoid
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
CategoryStruct.comp
Mon.Hom.hom
β€”β€”
yonedaMon_naturality πŸ“–mathematicalβ€”DFunLike.coe
Functor.obj
Opposite
Category.opposite
MonCat
MonCat.instCategory
yonedaMonObj
Opposite.op
MonCat.carrier
ConcreteCategory.hom
MonoidHom
MulOneClass.toMulOne
Monoid.toMulOneClass
MonCat.str
MonoidHom.instFunLike
MonCat.instConcreteCategoryMonoidHomCarrier
NatTrans.app
CategoryStruct.comp
Category.toCategoryStruct
Opposite.unop
β€”NatTrans.naturality
yonedaMon_naturality_assoc πŸ“–mathematicalβ€”CategoryStruct.comp
Category.toCategoryStruct
DFunLike.coe
MonoidHom
MonCat.carrier
Functor.obj
Opposite
Category.opposite
MonCat
MonCat.instCategory
yonedaMonObj
Opposite.op
MulOneClass.toMulOne
Monoid.toMulOneClass
MonCat.str
ConcreteCategory.hom
MonoidHom.instFunLike
MonCat.instConcreteCategoryMonoidHomCarrier
NatTrans.app
β€”Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
yonedaMon_naturality
yonedaMon_obj πŸ“–mathematicalβ€”Functor.obj
Mon
SemiCartesianMonoidalCategory.toMonoidalCategory
CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Mon.instCategory
Functor
Opposite
Category.opposite
MonCat
MonCat.instCategory
Functor.category
yonedaMon
yonedaMonObj
Mon.X
Mon.mon
β€”β€”

CategoryTheory.AddMon

Definitions

NameCategoryTheorems
instAddMonObjOfIsCommAddMonObjX πŸ“–CompOp
6 mathmath: instIsCommAddMonObj, Hom.hom_add, hom_zero, hom_add, Hom.hom_zero, Hom.hom_nsmul
instCartesianMonoidalCategory πŸ“–CompOp
6 mathmath: lift_hom, Hom.hom_add, snd_hom, Hom.hom_zero, Hom.hom_nsmul, fst_hom
uniqueHomToTrivial πŸ“–CompOp
1 mathmath: uniqueHomToTrivial_default_hom

Theorems

NameKindAssumesProvesValidatesDepends On
fst_hom πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instCartesianMonoidalCategory
CategoryTheory.SemiCartesianMonoidalCategory.fst
X
β€”β€”
hom_add πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
monMonoidal
CategoryTheory.AddMonObj.add
instAddMonObjOfIsCommAddMonObjX
X
addMon
β€”β€”
hom_zero πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.AddMon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
monMonoidal
CategoryTheory.AddMonObj.zero
instAddMonObjOfIsCommAddMonObjX
X
addMon
β€”β€”
instIsCommAddMonObj πŸ“–mathematicalβ€”CategoryTheory.IsCommAddMonObj
CategoryTheory.AddMon
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
instCategory
monMonoidal
CategoryTheory.SymmetricCategory.toBraidedCategory
instSymmetricCategory
CategoryTheory.CartesianMonoidalCategory.toSymmetricCategory
instAddMonObjOfIsCommAddMonObjX
β€”Hom.ext'
CategoryTheory.IsCommAddMonObj.add_comm
lift_hom πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
X
β€”β€”
snd_hom πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.AddMon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instCartesianMonoidalCategory
CategoryTheory.SemiCartesianMonoidalCategory.snd
X
β€”β€”
uniqueHomToTrivial_default_hom πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
trivial
Quiver.Hom
CategoryTheory.AddMon
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
instCategory
Unique.toInhabited
uniqueHomToTrivial
CategoryTheory.SemiCartesianMonoidalCategory.toUnit
X
β€”β€”

CategoryTheory.AddMon.Hom

Theorems

NameKindAssumesProvesValidatesDepends On
hom_add πŸ“–mathematicalβ€”hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Quiver.Hom
CategoryTheory.AddMon
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.AddMon.instCategory
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
CategoryTheory.AddMon.instCartesianMonoidalCategory
CategoryTheory.AddMon.instAddMonObjOfIsCommAddMonObjX
CategoryTheory.AddMon.X
CategoryTheory.AddMon.addMon
β€”β€”
hom_nsmul πŸ“–mathematicalβ€”hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Quiver.Hom
CategoryTheory.AddMon
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.AddMon.instCategory
AddMonoid.toNSMul
CategoryTheory.Hom.addMonoid
CategoryTheory.AddMon.instCartesianMonoidalCategory
CategoryTheory.AddMon.instAddMonObjOfIsCommAddMonObjX
CategoryTheory.AddMon.X
CategoryTheory.AddMon.addMon
β€”zero_nsmul
succ_nsmul
hom_zero πŸ“–mathematicalβ€”hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Quiver.Hom
CategoryTheory.AddMon
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.AddMon.instCategory
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
CategoryTheory.AddMon.instCartesianMonoidalCategory
CategoryTheory.AddMon.instAddMonObjOfIsCommAddMonObjX
CategoryTheory.AddMon.X
CategoryTheory.AddMon.addMon
β€”β€”

CategoryTheory.AddMonObj

Definitions

NameCategoryTheorems
ofRepresentableBy πŸ“–CompOp
5 mathmath: ofRepresentableBy_add, CategoryTheory.yonedaAddMonObjIsoOfRepresentableBy_hom_app_hom_apply, CategoryTheory.yonedaAddMonObjIsoOfRepresentableBy_inv_app_hom_apply, ofRepresentableBy_zero, ofRepresentableBy_yonedaAddMonObjRepresentableBy

Theorems

NameKindAssumesProvesValidatesDepends On
add_comp πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
β€”CategoryTheory.Category.assoc
CategoryTheory.IsAddMonHom.add_hom
CategoryTheory.CartesianMonoidalCategory.lift_map_assoc
add_comp_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
add_comp
add_eq_add πŸ“–mathematicalβ€”add
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
CategoryTheory.SemiCartesianMonoidalCategory.fst
CategoryTheory.SemiCartesianMonoidalCategory.snd
β€”CategoryTheory.CartesianMonoidalCategory.lift_fst_snd
CategoryTheory.Category.id_comp
comp_add πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
β€”AddMonoidHom.map_add
comp_add_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_add
comp_nsmul πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddMonoid.toNSMul
CategoryTheory.Hom.addMonoid
β€”zero_nsmul
comp_zero
succ_nsmul
comp_add
comp_nsmul_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddMonoid.toNSMul
CategoryTheory.Hom.addMonoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_nsmul
comp_zero πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
β€”AddMonoidHom.map_zero
comp_zero_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_zero
instIsAddMonHomAddOfIsCommAddMonObj πŸ“–mathematicalβ€”CategoryTheory.IsAddMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.AddMon.instAddMonObjTensorObj
add
β€”CategoryTheory.Category.assoc
add_zero_hom
CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unique
CategoryTheory.Iso.inv_hom_id_assoc
add_add_add_comm
instIsAddMonHomFst πŸ“–mathematicalβ€”CategoryTheory.IsAddMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.AddMon.instAddMonObjTensorObj
CategoryTheory.SemiCartesianMonoidalCategory.fst
β€”CategoryTheory.Category.assoc
CategoryTheory.CartesianMonoidalCategory.tensorHom_fst
CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst_assoc
CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unit
CategoryTheory.Category.id_comp
CategoryTheory.CartesianMonoidalCategory.tensorΞΌ_fst_assoc
instIsAddMonHomLift πŸ“–mathematicalβ€”CategoryTheory.IsAddMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.AddMon.instAddMonObjTensorObj
CategoryTheory.CartesianMonoidalCategory.lift
β€”CategoryTheory.CartesianMonoidalCategory.comp_lift
CategoryTheory.IsAddMonHom.zero_hom
CategoryTheory.CartesianMonoidalCategory.hom_ext
CategoryTheory.CartesianMonoidalCategory.lift_fst
CategoryTheory.Category.assoc
CategoryTheory.CartesianMonoidalCategory.tensorHom_fst
CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst_assoc
CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unit
CategoryTheory.Category.id_comp
CategoryTheory.CartesianMonoidalCategory.lift_snd
CategoryTheory.CartesianMonoidalCategory.tensorHom_snd
CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd_assoc
CategoryTheory.IsAddMonHom.add_hom
CategoryTheory.CartesianMonoidalCategory.tensorΞΌ_fst_assoc
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom_assoc
CategoryTheory.CartesianMonoidalCategory.tensorΞΌ_snd_assoc
instIsAddMonHomSnd πŸ“–mathematicalβ€”CategoryTheory.IsAddMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.AddMon.instAddMonObjTensorObj
CategoryTheory.SemiCartesianMonoidalCategory.snd
β€”CategoryTheory.Category.assoc
CategoryTheory.CartesianMonoidalCategory.tensorHom_snd
CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd_assoc
CategoryTheory.CartesianMonoidalCategory.tensorΞΌ_snd_assoc
instIsAddMonHomToAddUnit πŸ“–mathematicalβ€”CategoryTheory.IsAddMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorAddUnit
CategoryTheory.SemiCartesianMonoidalCategory.toUnit
β€”CategoryTheory.SemiCartesianMonoidalCategory.comp_toUnit
CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unit
Unique.instSubsingleton
instIsAddMonHomZero πŸ“–mathematicalβ€”CategoryTheory.IsAddMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorAddUnit
zero
β€”CategoryTheory.Category.id_comp
add_zero_hom
CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unique
lift_comp_zero_left πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
CategoryTheory.MonoidalCategoryStruct.tensorUnit
zero
add
β€”CategoryTheory.whisker_eq
zero_add
CategoryTheory.CartesianMonoidalCategory.lift_leftUnitor_hom
CategoryTheory.CartesianMonoidalCategory.lift_whiskerRight_assoc
lift_comp_zero_left_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
CategoryTheory.MonoidalCategoryStruct.tensorUnit
zero
add
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
lift_comp_zero_left
lift_comp_zero_right πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
CategoryTheory.MonoidalCategoryStruct.tensorUnit
zero
add
β€”CategoryTheory.whisker_eq
add_zero
CategoryTheory.CartesianMonoidalCategory.lift_rightUnitor_hom
CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeft_assoc
lift_comp_zero_right_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
CategoryTheory.MonoidalCategoryStruct.tensorUnit
zero
add
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
lift_comp_zero_right
lift_lift_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
add
β€”CategoryTheory.whisker_eq
add_assoc
CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeft_assoc
CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom_assoc
CategoryTheory.CartesianMonoidalCategory.lift_whiskerRight_assoc
nsmul_comp πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddMonoid.toNSMul
CategoryTheory.Hom.addMonoid
β€”zero_nsmul
zero_comp
succ_nsmul
add_comp
nsmul_comp_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddMonoid.toNSMul
CategoryTheory.Hom.addMonoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
nsmul_comp
ofRepresentableBy_add πŸ“–mathematicalβ€”add
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
ofRepresentableBy
DFunLike.coe
Equiv
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
CategoryTheory.types
CategoryTheory.Functor.comp
AddMonCat
AddMonCat.instCategory
CategoryTheory.forget
AddMonoidHom
AddMonCat.carrier
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonCat.str
AddMonoidHom.instFunLike
AddMonCat.instConcreteCategoryAddMonoidHomCarrier
Opposite.op
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
CategoryTheory.Functor.RepresentableBy.homEquiv
AddZero.toAdd
AddMonCat.addMonoidObj
CategoryTheory.SemiCartesianMonoidalCategory.fst
CategoryTheory.SemiCartesianMonoidalCategory.snd
β€”β€”
ofRepresentableBy_yonedaAddMonObjRepresentableBy πŸ“–mathematicalβ€”ofRepresentableBy
CategoryTheory.yonedaAddMonObj
CategoryTheory.yonedaAddMonObjRepresentableBy
β€”ext
CategoryTheory.CartesianMonoidalCategory.lift_fst_snd
CategoryTheory.Category.id_comp
ofRepresentableBy_zero πŸ“–mathematicalβ€”zero
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
ofRepresentableBy
DFunLike.coe
Equiv
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
CategoryTheory.types
CategoryTheory.Functor.comp
AddMonCat
AddMonCat.instCategory
CategoryTheory.forget
AddMonoidHom
AddMonCat.carrier
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonCat.str
AddMonoidHom.instFunLike
AddMonCat.instConcreteCategoryAddMonoidHomCarrier
Opposite.op
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
CategoryTheory.Functor.RepresentableBy.homEquiv
AddZero.toZero
AddMonCat.addMonoidObj
β€”β€”
zero_comp πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
β€”CategoryTheory.Category.assoc
CategoryTheory.IsAddMonHom.zero_hom
zero_comp_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
zero_comp
zero_eq_zero πŸ“–mathematicalβ€”zero
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
β€”CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unique
CategoryTheory.Category.id_comp

CategoryTheory.Functor

Definitions

NameCategoryTheorems
homAddMonoidHom πŸ“–CompOp
1 mathmath: homAddMonoidHom_apply
homMonoidHom πŸ“–CompOp
1 mathmath: homMonoidHom_apply

Theorems

NameKindAssumesProvesValidatesDepends On
homAddMonoidHom_apply πŸ“–mathematicalβ€”DFunLike.coe
AddMonoidHom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
obj
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
addMonObjObj
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Monoidal.toLaxMonoidal
AddMonoidHom.instFunLike
homAddMonoidHom
map
β€”β€”
homMonoidHom_apply πŸ“–mathematicalβ€”DFunLike.coe
MonoidHom
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
obj
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
monObjObj
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Monoidal.toLaxMonoidal
MonoidHom.instFunLike
homMonoidHom
map
β€”β€”
map_add' πŸ“–mathematicalβ€”map
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
obj
addMonObjObj
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Monoidal.toLaxMonoidal
β€”map_comp
Monoidal.lift_ΞΌ_assoc
map_mul πŸ“–mathematicalβ€”map
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
obj
monObjObj
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Monoidal.toLaxMonoidal
β€”map_comp
Monoidal.lift_ΞΌ_assoc
map_one πŸ“–mathematicalβ€”map
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
obj
monObjObj
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Monoidal.toLaxMonoidal
β€”map_comp
Monoidal.toUnit_Ξ΅_assoc
map_zero' πŸ“–mathematicalβ€”map
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
obj
addMonObjObj
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Monoidal.toLaxMonoidal
β€”map_comp
Monoidal.toUnit_Ξ΅_assoc

CategoryTheory.Functor.FullyFaithful

Definitions

NameCategoryTheorems
homAddEquiv πŸ“–CompOp
2 mathmath: homAddEquiv_symm_apply, homAddEquiv_apply
homMulEquiv πŸ“–CompOp
2 mathmath: homMulEquiv_apply, homMulEquiv_symm_apply

Theorems

NameKindAssumesProvesValidatesDepends On
homAddEquiv_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
CategoryTheory.Functor.addMonObjObj
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Functor.Monoidal.toLaxMonoidal
EquivLike.toFunLike
AddEquiv.instEquivLike
homAddEquiv
CategoryTheory.Functor.map
β€”β€”
homAddEquiv_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
CategoryTheory.Hom.addMonoid
CategoryTheory.Functor.addMonObjObj
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Functor.Monoidal.toLaxMonoidal
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
homAddEquiv
preimage
β€”β€”
homMulEquiv_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
CategoryTheory.Functor.monObjObj
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Functor.Monoidal.toLaxMonoidal
EquivLike.toFunLike
MulEquiv.instEquivLike
homMulEquiv
CategoryTheory.Functor.map
β€”β€”
homMulEquiv_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Functor.obj
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
CategoryTheory.Functor.monObjObj
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Functor.Monoidal.toLaxMonoidal
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
homMulEquiv
preimage
β€”β€”

CategoryTheory.Hom

Definitions

NameCategoryTheorems
addCommMonoid πŸ“–CompOpβ€”
addEquivCongrRight πŸ“–CompOp
2 mathmath: addEquivCongrRight_symm_apply, addEquivCongrRight_apply
addMonoid πŸ“–CompOp
31 mathmath: CategoryTheory.yonedaAddMonObjIsoOfRepresentableBy_hom_app_hom_apply, CategoryTheory.AddMonObj.add_eq_add, CategoryTheory.AddMonObj.zero_comp, CategoryTheory.AddMon.Hom.hom_add, CategoryTheory.AddMonObj.add_comp, CategoryTheory.AddMonObj.comp_nsmul, CategoryTheory.AddMonObj.add_comp_assoc, CategoryTheory.Functor.map_add', CategoryTheory.AddMonObj.comp_add, CategoryTheory.AddMonObj.nsmul_comp_assoc, CategoryTheory.yonedaAddMonObjIsoOfRepresentableBy_inv_app_hom_apply, CategoryTheory.isCommAddMonObj_iff_isAddCommutative, addEquivCongrRight_symm_apply, CategoryTheory.AddMonObj.zero_eq_zero, CategoryTheory.Functor.FullyFaithful.homAddEquiv_symm_apply, CategoryTheory.yonedaAddMonObj_map, add_def, addEquivCongrRight_apply, zero_def, CategoryTheory.AddMon.Hom.hom_zero, CategoryTheory.AddMonObj.comp_nsmul_assoc, CategoryTheory.Functor.map_zero', CategoryTheory.Functor.homAddMonoidHom_apply, CategoryTheory.AddMonObj.comp_zero_assoc, CategoryTheory.AddMonObj.comp_zero, CategoryTheory.AddMon.Hom.hom_nsmul, CategoryTheory.AddMonObj.comp_add_assoc, CategoryTheory.AddMonObj.zero_comp_assoc, CategoryTheory.AddMonObj.nsmul_comp, CategoryTheory.Functor.FullyFaithful.homAddEquiv_apply, CategoryTheory.yonedaAddMon_map_app
commMonoid πŸ“–CompOpβ€”
monoid πŸ“–CompOp
44 mathmath: CategoryTheory.Functor.map_mul, CategoryTheory.shrinkYonedaMonObjObjEquiv_symm_comp, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, CategoryTheory.Functor.FullyFaithful.homMulEquiv_apply, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, CategoryTheory.MonObj.comp_mul_assoc, CategoryTheory.GrpObj.lift_conj_eq_mul_mul_inv, CategoryTheory.MonObj.comp_one, CategoryTheory.MonObj.one_comp_assoc, CategoryTheory.yonedaMonObj_map, CategoryTheory.MonObj.mul_comp, mul_def, CategoryTheory.GrpObj.lift_conj_eq_mul_mul_inv_assoc, CategoryTheory.yonedaMon_map_app, CategoryTheory.MonObj.one_comp, CategoryTheory.shrinkYonedaMon_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.MonObj.comp_pow, CategoryTheory.Grp.Hom.hom_pow, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv, mulEquivCongrRight_symm_apply, CategoryTheory.MonObj.mul_comp_assoc, CategoryTheory.isCommMonObj_iff_isMulCommutative, CategoryTheory.Mon.Hom.hom_mul, CategoryTheory.Functor.FullyFaithful.homMulEquiv_symm_apply, CategoryTheory.shrinkYonedaGrp_obj_map_shrinkYonedaGrpObjObjEquiv_symm, CategoryTheory.MonObj.pow_comp_assoc, CategoryTheory.Grp.Hom.hom_mul, CategoryTheory.Mon.Hom.hom_pow, CategoryTheory.MonObj.comp_mul, CategoryTheory.MonObj.comp_one_assoc, CategoryTheory.GrpObj.lift_commutator_eq_mul_mul_inv_inv_assoc, CategoryTheory.MonObj.pow_comp, one_def, CategoryTheory.Functor.homMonoidHom_apply, CategoryTheory.shrinkYonedaMon_obj_map_shrinkYonedaMonObjObjEquiv_symm, CategoryTheory.MonObj.one_eq_one, mulEquivCongrRight_apply, CategoryTheory.Grp.Hom.hom_one, CategoryTheory.MonObj.comp_pow_assoc, CategoryTheory.shrinkYonedaGrpObjObjEquiv_symm_comp, CategoryTheory.Functor.map_one, CategoryTheory.MonObj.mul_eq_mul, CategoryTheory.shrinkYonedaGrp_map_app_shrinkYonedaObjObjEquiv_symm, CategoryTheory.Mon.Hom.hom_one
mulEquivCongrRight πŸ“–CompOp
2 mathmath: mulEquivCongrRight_symm_apply, mulEquivCongrRight_apply

Theorems

NameKindAssumesProvesValidatesDepends On
addEquivCongrRight_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
addMonoid
EquivLike.toFunLike
AddEquiv.instEquivLike
addEquivCongrRight
AddMonoidHom
AddMonCat.carrier
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
AddMonCat
AddMonCat.instCategory
CategoryTheory.AddMon
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.yonedaAddMon
Opposite.op
AddMonCat.str
AddMonoidHom.instFunLike
AddMonCat.Hom.hom
CategoryTheory.yonedaAddMonObj
CategoryTheory.AddMon.addMon
AddMonCat.ofHom
CategoryTheory.AddMon.X
Opposite.unop
AddZero.toZero
CategoryTheory.CategoryStruct.comp
CategoryTheory.Iso.hom
CategoryTheory.AddMon.mkIso'
β€”β€”
addEquivCongrRight_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
AddEquiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
addMonoid
EquivLike.toFunLike
AddEquiv.instEquivLike
AddEquiv.symm
addEquivCongrRight
AddMonoidHom
AddMonCat.carrier
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
AddMonCat
AddMonCat.instCategory
CategoryTheory.AddMon
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.AddMon.instCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.yonedaAddMon
Opposite.op
AddMonCat.str
AddMonoidHom.instFunLike
AddMonCat.Hom.hom
CategoryTheory.yonedaAddMonObj
CategoryTheory.AddMon.addMon
AddMonCat.ofHom
CategoryTheory.AddMon.X
Opposite.unop
AddZero.toZero
CategoryTheory.CategoryStruct.comp
CategoryTheory.Iso.inv
CategoryTheory.AddMon.mkIso'
β€”β€”
add_def πŸ“–mathematicalβ€”Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
addMonoid
CategoryTheory.CategoryStruct.comp
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
CategoryTheory.AddMonObj.add
β€”β€”
mulEquivCongrRight_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
monoid
EquivLike.toFunLike
MulEquiv.instEquivLike
mulEquivCongrRight
MonoidHom
MonCat.carrier
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
MonCat
MonCat.instCategory
CategoryTheory.Mon
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Mon.instCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.yonedaMon
Opposite.op
MonCat.str
MonoidHom.instFunLike
MonCat.Hom.hom
CategoryTheory.yonedaMonObj
CategoryTheory.Mon.mon
MonCat.ofHom
CategoryTheory.Mon.X
Opposite.unop
MulOne.toOne
CategoryTheory.CategoryStruct.comp
CategoryTheory.Iso.hom
CategoryTheory.Mon.mkIso'
β€”β€”
mulEquivCongrRight_symm_apply πŸ“–mathematicalβ€”DFunLike.coe
MulEquiv
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
monoid
EquivLike.toFunLike
MulEquiv.instEquivLike
MulEquiv.symm
mulEquivCongrRight
MonoidHom
MonCat.carrier
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
MonCat
MonCat.instCategory
CategoryTheory.Mon
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.Mon.instCategory
CategoryTheory.Functor
CategoryTheory.Functor.category
CategoryTheory.yonedaMon
Opposite.op
MonCat.str
MonoidHom.instFunLike
MonCat.Hom.hom
CategoryTheory.yonedaMonObj
CategoryTheory.Mon.mon
MonCat.ofHom
CategoryTheory.Mon.X
Opposite.unop
MulOne.toOne
CategoryTheory.CategoryStruct.comp
CategoryTheory.Iso.inv
CategoryTheory.Mon.mkIso'
β€”β€”
mul_def πŸ“–mathematicalβ€”Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
monoid
CategoryTheory.CategoryStruct.comp
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
CategoryTheory.MonObj.mul
β€”β€”
one_def πŸ“–mathematicalβ€”Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
monoid
CategoryTheory.CategoryStruct.comp
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.SemiCartesianMonoidalCategory.toUnit
CategoryTheory.MonObj.one
β€”β€”
zero_def πŸ“–mathematicalβ€”Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
addMonoid
CategoryTheory.CategoryStruct.comp
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.SemiCartesianMonoidalCategory.toUnit
CategoryTheory.AddMonObj.zero
β€”β€”

CategoryTheory.Mon

Definitions

NameCategoryTheorems
instCartesianMonoidalCategory πŸ“–CompOp
10 mathmath: CategoryTheory.Grp.lift_hom, lift_hom, fst_hom, CategoryTheory.Grp.Hom.hom_pow, Hom.hom_mul, CategoryTheory.Grp.Hom.hom_mul, Hom.hom_pow, CategoryTheory.Grp.Hom.hom_one, snd_hom, Hom.hom_one
instMonObjOfIsCommMonObjX πŸ“–CompOp
9 mathmath: CategoryTheory.Grp.Hom.hom_pow, instIsCommMonObj, Hom.hom_mul, CategoryTheory.Grp.Hom.hom_mul, Hom.hom_pow, hom_mul, CategoryTheory.Grp.Hom.hom_one, hom_one, Hom.hom_one
uniqueHomToTrivial πŸ“–CompOp
1 mathmath: uniqueHomToTrivial_default_hom

Theorems

NameKindAssumesProvesValidatesDepends On
fst_hom πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instCartesianMonoidalCategory
CategoryTheory.SemiCartesianMonoidalCategory.fst
X
β€”β€”
hom_mul πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
monMonoidal
CategoryTheory.MonObj.mul
instMonObjOfIsCommMonObjX
X
mon
β€”β€”
hom_one πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.Mon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
monMonoidal
CategoryTheory.MonObj.one
instMonObjOfIsCommMonObjX
X
mon
β€”β€”
instIsCommMonObj πŸ“–mathematicalβ€”CategoryTheory.IsCommMonObj
CategoryTheory.Mon
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
instCategory
monMonoidal
CategoryTheory.SymmetricCategory.toBraidedCategory
instSymmetricCategory
CategoryTheory.CartesianMonoidalCategory.toSymmetricCategory
instMonObjOfIsCommMonObjX
β€”Hom.ext'
CategoryTheory.IsCommMonObj.mul_comm
lift_hom πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
X
β€”β€”
snd_hom πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.Mon
instCategory
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instCartesianMonoidalCategory
CategoryTheory.SemiCartesianMonoidalCategory.snd
X
β€”β€”
uniqueHomToTrivial_default_hom πŸ“–mathematicalβ€”Hom.hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
trivial
Quiver.Hom
CategoryTheory.Mon
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
instCategory
Unique.toInhabited
uniqueHomToTrivial
CategoryTheory.SemiCartesianMonoidalCategory.toUnit
X
β€”β€”

CategoryTheory.Mon.Hom

Theorems

NameKindAssumesProvesValidatesDepends On
hom_mul πŸ“–mathematicalβ€”hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Quiver.Hom
CategoryTheory.Mon
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Mon.instCategory
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
CategoryTheory.Mon.instCartesianMonoidalCategory
CategoryTheory.Mon.instMonObjOfIsCommMonObjX
CategoryTheory.Mon.X
CategoryTheory.Mon.mon
β€”β€”
hom_one πŸ“–mathematicalβ€”hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Quiver.Hom
CategoryTheory.Mon
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Mon.instCategory
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
CategoryTheory.Mon.instCartesianMonoidalCategory
CategoryTheory.Mon.instMonObjOfIsCommMonObjX
CategoryTheory.Mon.X
CategoryTheory.Mon.mon
β€”β€”
hom_pow πŸ“–mathematicalβ€”hom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Quiver.Hom
CategoryTheory.Mon
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.Mon.instCategory
Monoid.toPow
CategoryTheory.Hom.monoid
CategoryTheory.Mon.instCartesianMonoidalCategory
CategoryTheory.Mon.instMonObjOfIsCommMonObjX
CategoryTheory.Mon.X
CategoryTheory.Mon.mon
β€”pow_zero
pow_succ

CategoryTheory.MonObj

Definitions

NameCategoryTheorems
ofRepresentableBy πŸ“–CompOp
6 mathmath: CategoryTheory.yonedaMonObjIsoOfRepresentableBy_hom_app_hom_apply, CategoryTheory.yonedaMonObjIsoOfRepresentableBy_inv_app_hom_apply, ofRepresentableBy_one, CategoryTheory.IsCommMonObj.ofRepresentableBy, ofRepresentableBy_yonedaMonObjRepresentableBy, ofRepresentableBy_mul

Theorems

NameKindAssumesProvesValidatesDepends On
comp_mul πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
β€”MonoidHom.map_mul
comp_mul_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_mul
comp_one πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
β€”MonoidHom.map_one
comp_one_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_one
comp_pow πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
Monoid.toPow
CategoryTheory.Hom.monoid
β€”pow_zero
comp_one
pow_succ
comp_mul
comp_pow_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
Monoid.toPow
CategoryTheory.Hom.monoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
comp_pow
instIsMonHomFst πŸ“–mathematicalβ€”CategoryTheory.IsMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Mon.instMonObjTensorObj
CategoryTheory.SemiCartesianMonoidalCategory.fst
β€”CategoryTheory.Category.assoc
CategoryTheory.CartesianMonoidalCategory.tensorHom_fst
CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst_assoc
CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unit
CategoryTheory.Category.id_comp
CategoryTheory.CartesianMonoidalCategory.tensorΞΌ_fst_assoc
instIsMonHomLift πŸ“–mathematicalβ€”CategoryTheory.IsMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Mon.instMonObjTensorObj
CategoryTheory.CartesianMonoidalCategory.lift
β€”CategoryTheory.CartesianMonoidalCategory.comp_lift
CategoryTheory.IsMonHom.one_hom
CategoryTheory.CartesianMonoidalCategory.hom_ext
CategoryTheory.CartesianMonoidalCategory.lift_fst
CategoryTheory.Category.assoc
CategoryTheory.CartesianMonoidalCategory.tensorHom_fst
CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_fst_assoc
CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unit
CategoryTheory.Category.id_comp
CategoryTheory.CartesianMonoidalCategory.lift_snd
CategoryTheory.CartesianMonoidalCategory.tensorHom_snd
CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd_assoc
CategoryTheory.IsMonHom.mul_hom
CategoryTheory.CartesianMonoidalCategory.tensorΞΌ_fst_assoc
CategoryTheory.MonoidalCategory.tensorHom_comp_tensorHom_assoc
CategoryTheory.CartesianMonoidalCategory.tensorΞΌ_snd_assoc
instIsMonHomMulOfIsCommMonObj πŸ“–mathematicalβ€”CategoryTheory.IsMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Mon.instMonObjTensorObj
mul
β€”CategoryTheory.Category.assoc
mul_one_hom
CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unique
CategoryTheory.Iso.inv_hom_id_assoc
mul_mul_mul_comm
instIsMonHomOne πŸ“–mathematicalβ€”CategoryTheory.IsMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorUnit
one
β€”CategoryTheory.Category.id_comp
mul_one_hom
CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unique
instIsMonHomSnd πŸ“–mathematicalβ€”CategoryTheory.IsMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.Mon.instMonObjTensorObj
CategoryTheory.SemiCartesianMonoidalCategory.snd
β€”CategoryTheory.Category.assoc
CategoryTheory.CartesianMonoidalCategory.tensorHom_snd
CategoryTheory.CartesianMonoidalCategory.leftUnitor_inv_snd_assoc
CategoryTheory.CartesianMonoidalCategory.tensorΞΌ_snd_assoc
instIsMonHomToUnit πŸ“–mathematicalβ€”CategoryTheory.IsMonHom
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
instTensorUnit
CategoryTheory.SemiCartesianMonoidalCategory.toUnit
β€”CategoryTheory.SemiCartesianMonoidalCategory.comp_toUnit
CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unit
Unique.instSubsingleton
lift_comp_one_left πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
CategoryTheory.MonoidalCategoryStruct.tensorUnit
one
mul
β€”CategoryTheory.whisker_eq
one_mul
CategoryTheory.CartesianMonoidalCategory.lift_leftUnitor_hom
CategoryTheory.CartesianMonoidalCategory.lift_whiskerRight_assoc
lift_comp_one_left_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
CategoryTheory.MonoidalCategoryStruct.tensorUnit
one
mul
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
lift_comp_one_left
lift_comp_one_right πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
CategoryTheory.MonoidalCategoryStruct.tensorUnit
one
mul
β€”CategoryTheory.whisker_eq
mul_one
CategoryTheory.CartesianMonoidalCategory.lift_rightUnitor_hom
CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeft_assoc
lift_comp_one_right_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
CategoryTheory.MonoidalCategoryStruct.tensorUnit
one
mul
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
lift_comp_one_right
lift_lift_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.lift
mul
β€”CategoryTheory.whisker_eq
mul_assoc
CategoryTheory.CartesianMonoidalCategory.lift_whiskerLeft_assoc
CategoryTheory.CartesianMonoidalCategory.lift_lift_associator_hom_assoc
CategoryTheory.CartesianMonoidalCategory.lift_whiskerRight_assoc
mul_comp πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
β€”CategoryTheory.Category.assoc
CategoryTheory.IsMonHom.mul_hom
CategoryTheory.CartesianMonoidalCategory.lift_map_assoc
mul_comp_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
mul_comp
mul_eq_mul πŸ“–mathematicalβ€”mul
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
CategoryTheory.SemiCartesianMonoidalCategory.fst
CategoryTheory.SemiCartesianMonoidalCategory.snd
β€”CategoryTheory.CartesianMonoidalCategory.lift_fst_snd
CategoryTheory.Category.id_comp
ofRepresentableBy_mul πŸ“–mathematicalβ€”mul
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
ofRepresentableBy
DFunLike.coe
Equiv
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
CategoryTheory.types
CategoryTheory.Functor.comp
MonCat
MonCat.instCategory
CategoryTheory.forget
MonoidHom
MonCat.carrier
MulOneClass.toMulOne
Monoid.toMulOneClass
MonCat.str
MonoidHom.instFunLike
MonCat.instConcreteCategoryMonoidHomCarrier
Opposite.op
CategoryTheory.MonoidalCategoryStruct.tensorObj
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
CategoryTheory.Functor.RepresentableBy.homEquiv
MulOne.toMul
MonCat.monoidObj
CategoryTheory.SemiCartesianMonoidalCategory.fst
CategoryTheory.SemiCartesianMonoidalCategory.snd
β€”β€”
ofRepresentableBy_one πŸ“–mathematicalβ€”one
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
ofRepresentableBy
DFunLike.coe
Equiv
CategoryTheory.Functor.obj
Opposite
CategoryTheory.Category.opposite
CategoryTheory.types
CategoryTheory.Functor.comp
MonCat
MonCat.instCategory
CategoryTheory.forget
MonoidHom
MonCat.carrier
MulOneClass.toMulOne
Monoid.toMulOneClass
MonCat.str
MonoidHom.instFunLike
MonCat.instConcreteCategoryMonoidHomCarrier
Opposite.op
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
CategoryTheory.Functor.RepresentableBy.homEquiv
MulOne.toOne
MonCat.monoidObj
β€”β€”
ofRepresentableBy_yonedaMonObjRepresentableBy πŸ“–mathematicalβ€”ofRepresentableBy
CategoryTheory.yonedaMonObj
CategoryTheory.yonedaMonObjRepresentableBy
β€”ext
CategoryTheory.CartesianMonoidalCategory.lift_fst_snd
CategoryTheory.Category.id_comp
one_comp πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
β€”CategoryTheory.Category.assoc
CategoryTheory.IsMonHom.one_hom
one_comp_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
one_comp
one_eq_one πŸ“–mathematicalβ€”one
CategoryTheory.SemiCartesianMonoidalCategory.toMonoidalCategory
CategoryTheory.CartesianMonoidalCategory.toSemiCartesianMonoidalCategory
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
CategoryTheory.MonoidalCategoryStruct.tensorUnit
CategoryTheory.MonoidalCategory.toMonoidalCategoryStruct
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CategoryTheory.Hom.monoid
β€”CategoryTheory.SemiCartesianMonoidalCategory.toUnit_unique
CategoryTheory.Category.id_comp
pow_comp πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
Monoid.toPow
CategoryTheory.Hom.monoid
β€”pow_zero
one_comp
pow_succ
mul_comp
pow_comp_assoc πŸ“–mathematicalβ€”CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
Monoid.toPow
CategoryTheory.Hom.monoid
β€”CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
pow_comp

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