Documentation Verification Report

Resolution

šŸ“ Source: Mathlib/CategoryTheory/Preadditive/Injective/Resolution.lean

Statistics

MetricCount
DefinitionsHasInjectiveResolution, HasInjectiveResolutions, InjectiveResolution, hom, cocomplex, isLimitKernelFork, kernelFork, self, ι
9
Theoremsout, out, ι_comp_hom, ι_comp_hom_assoc, ι_f_zero_comp_hom_f_zero, ι_f_zero_comp_hom_f_zero_assoc, cocomplex_exactAt_succ, complex_d_comp, exact_succ, hasHomology, injective, instMonoFNatι, quasiIso, self_cocomplex, self_ι, ι_f_succ, ι_f_zero_comp_complex_d, ι_f_zero_comp_complex_d_assoc
18
Total27

CategoryTheory

Definitions

NameCategoryTheorems
HasInjectiveResolution šŸ“–CompData
2 mathmath: InjectiveResolution.instHasInjectiveResolution, HasInjectiveResolutions.out
HasInjectiveResolutions šŸ“–CompData
1 mathmath: InjectiveResolution.instHasInjectiveResolutions
InjectiveResolution šŸ“–CompData
1 mathmath: HasInjectiveResolution.out

CategoryTheory.HasInjectiveResolution

Theorems

NameKindAssumesProvesValidatesDepends On
out šŸ“–mathematical—CategoryTheory.InjectiveResolution——

CategoryTheory.HasInjectiveResolutions

Theorems

NameKindAssumesProvesValidatesDepends On
out šŸ“–mathematical—CategoryTheory.HasInjectiveResolution——

CategoryTheory.InjectiveResolution

Definitions

NameCategoryTheorems
cocomplex šŸ“–CompOp
69 mathmath: injective, Hom.hom'_f, extMk_comp_mkā‚€, homotopyEquiv_inv_ι, isoRightDerivedToHomotopyCategoryObj_inv_naturality_assoc, ι'_f_zero, iso_hom_naturality, toRightDerivedZero'_naturality_assoc, isoRightDerivedToHomotopyCategoryObj_inv_naturality, toRightDerivedZero'_comp_iCycles, complex_d_comp, desc_commutes_zero_assoc, CategoryTheory.instIsIsoToRightDerivedZero', comp_descHomotopyZeroSucc_assoc, toRightDerivedZero_eq, comp_descHomotopyZeroZero_assoc, extMk_surjective, Hom.ι_comp_hom_assoc, ι_f_succ, ι_f_zero_comp_complex_d_assoc, instIsIsoToRightDerivedZero'Self, add_extMk, extMk_zero, isoRightDerivedObj_hom_naturality, extMk_eq_zero_iff, ι_f_zero_comp_complex_d, toRightDerivedZero'_naturality, self_cocomplex, desc_commutes, desc_commutes_assoc, Hom.ι_f_zero_comp_hom_f_zero, iso_hom_naturality_assoc, isoRightDerivedObj_hom_naturality_assoc, isoRightDerivedObj_inv_naturality, ι'_f_zero_assoc, sub_extMk, cocomplex_exactAt_succ, isoRightDerivedToHomotopyCategoryObj_hom_naturality_assoc, Hom.hom'_f_assoc, mkā‚€_comp_extMk, extMk_hom, cochainComplex_d_assoc, comp_descHomotopyZeroOne_assoc, CategoryTheory.Functor.rightDerived_map_eq, desc_commutes_zero, comp_descHomotopyZeroOne, hasHomology, neg_extMk, iso_inv_naturality_assoc, isoRightDerivedToHomotopyCategoryObj_hom_naturality, Hom.ι_f_zero_comp_hom_f_zero_assoc, exact_succ, instMonoFNatι, comp_descHomotopyZeroZero, toRightDerivedZero'_comp_iCycles_assoc, homotopyEquiv_hom_ι_assoc, homotopyEquiv_hom_ι, exactā‚€, isoRightDerivedObj_inv_naturality_assoc, extEquivCohomologyClass_extMk, homotopyEquiv_inv_ι_assoc, comp_descHomotopyZeroSucc, rightDerivedToHomotopyCategory_app_eq, quasiIso, iso_inv_naturality, Hom.ι_comp_hom, descFOne_zero_comm, rightDerived_app_eq, cochainComplex_d
isLimitKernelFork šŸ“–CompOp—
kernelFork šŸ“–CompOp—
self šŸ“–CompOp
3 mathmath: self_ι, instIsIsoToRightDerivedZero'Self, self_cocomplex
ι šŸ“–CompOp
23 mathmath: homotopyEquiv_inv_ι, ι'_f_zero, self_ι, toRightDerivedZero'_comp_iCycles, desc_commutes_zero_assoc, Hom.ι_comp_hom_assoc, ι_f_succ, ι_f_zero_comp_complex_d_assoc, ι_f_zero_comp_complex_d, desc_commutes, desc_commutes_assoc, Hom.ι_f_zero_comp_hom_f_zero, ι'_f_zero_assoc, desc_commutes_zero, Hom.ι_f_zero_comp_hom_f_zero_assoc, instMonoFNatι, toRightDerivedZero'_comp_iCycles_assoc, homotopyEquiv_hom_ι_assoc, homotopyEquiv_hom_ι, exactā‚€, homotopyEquiv_inv_ι_assoc, quasiIso, Hom.ι_comp_hom

Theorems

NameKindAssumesProvesValidatesDepends On
cocomplex_exactAt_succ šŸ“–mathematical—HomologicalComplex.ExactAt
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
cocomplex
—AddRightCancelSemigroup.toIsRightCancelAdd
HomologicalComplex.instHasHomologyObjSingle
hasHomology
quasiIsoAt_iff_exactAt
CochainComplex.exactAt_succ_single_obj
QuasiIso.quasiIsoAt
quasiIso
complex_d_comp šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
HomologicalComplex.X
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
cocomplex
HomologicalComplex.d
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Limits.HasZeroMorphisms.zero
—AddRightCancelSemigroup.toIsRightCancelAdd
HomologicalComplex.d_comp_d
exact_succ šŸ“–mathematical—CategoryTheory.ShortComplex.Exact
HomologicalComplex.X
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
cocomplex
HomologicalComplex.d
HomologicalComplex.d_comp_d
—AddRightCancelSemigroup.toIsRightCancelAdd
HomologicalComplex.exactAt_iff'
CochainComplex.prev_nat_succ
CochainComplex.next
cocomplex_exactAt_succ
hasHomology šŸ“–mathematical—HomologicalComplex.HasHomology
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
cocomplex
——
injective šŸ“–mathematical—CategoryTheory.Injective
HomologicalComplex.X
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
cocomplex
——
instMonoFNatι šŸ“–mathematical—CategoryTheory.Mono
HomologicalComplex.X
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
CategoryTheory.Functor.obj
CochainComplex
HomologicalComplex.instCategory
CochainComplex.singleā‚€
cocomplex
HomologicalComplex.Hom.f
ι
—AddRightCancelSemigroup.toIsRightCancelAdd
CategoryTheory.Limits.mono_of_isLimit_fork
ι_f_succ
CategoryTheory.Limits.HasZeroObject.instMono
quasiIso šŸ“–mathematical—QuasiIso
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
CategoryTheory.Functor.obj
CochainComplex
HomologicalComplex.instCategory
CochainComplex.singleā‚€
cocomplex
ι
HomologicalComplex.instHasHomologyObjSingle
hasHomology
——
self_cocomplex šŸ“–mathematical—cocomplex
self
CategoryTheory.Functor.obj
CochainComplex
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
HomologicalComplex.instCategory
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
CochainComplex.singleā‚€
——
self_ι šŸ“–mathematical—ι
self
CategoryTheory.CategoryStruct.id
CochainComplex
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
CategoryTheory.Category.toCategoryStruct
HomologicalComplex.instCategory
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
CategoryTheory.Functor.obj
CochainComplex.singleā‚€
——
ι_f_succ šŸ“–mathematical—HomologicalComplex.Hom.f
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
CategoryTheory.Functor.obj
CochainComplex
HomologicalComplex.instCategory
CochainComplex.singleā‚€
cocomplex
ι
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Category.toCategoryStruct
HomologicalComplex.X
CategoryTheory.Limits.HasZeroMorphisms.zero
—CategoryTheory.Limits.IsZero.eq_of_src
AddRightCancelSemigroup.toIsRightCancelAdd
HomologicalComplex.isZero_single_obj_X
ι_f_zero_comp_complex_d šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
HomologicalComplex.X
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
CategoryTheory.Functor.obj
CochainComplex
HomologicalComplex.instCategory
CochainComplex.singleā‚€
cocomplex
HomologicalComplex.Hom.f
ι
HomologicalComplex.d
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Limits.HasZeroMorphisms.zero
—AddRightCancelSemigroup.toIsRightCancelAdd
HomologicalComplex.Hom.comm
ι_f_succ
CategoryTheory.Limits.comp_zero
ι_f_zero_comp_complex_d_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
HomologicalComplex.X
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
CategoryTheory.Functor.obj
CochainComplex
HomologicalComplex.instCategory
CochainComplex.singleā‚€
cocomplex
HomologicalComplex.Hom.f
ι
HomologicalComplex.d
Quiver.Hom
CategoryTheory.CategoryStruct.toQuiver
CategoryTheory.Limits.HasZeroMorphisms.zero
—AddRightCancelSemigroup.toIsRightCancelAdd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
ι_f_zero_comp_complex_d

CategoryTheory.InjectiveResolution.Hom

Definitions

NameCategoryTheorems
hom šŸ“–CompOp
7 mathmath: hom'_f, CategoryTheory.InjectiveResolution.extMk_comp_mkā‚€, ι_comp_hom_assoc, ι_f_zero_comp_hom_f_zero, hom'_f_assoc, ι_f_zero_comp_hom_f_zero_assoc, ι_comp_hom

Theorems

NameKindAssumesProvesValidatesDepends On
ι_comp_hom šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CochainComplex
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
CategoryTheory.Category.toCategoryStruct
HomologicalComplex.instCategory
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelSemigroup.toIsRightCancelAdd
CategoryTheory.Functor.obj
CochainComplex.singleā‚€
CategoryTheory.InjectiveResolution.cocomplex
CategoryTheory.InjectiveResolution.ι
hom
CategoryTheory.Functor.map
—HomologicalComplex.from_single_hom_ext
AddRightCancelSemigroup.toIsRightCancelAdd
ι_f_zero_comp_hom_f_zero
CochainComplex.singleā‚€_map_f_zero
ι_comp_hom_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CochainComplex
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
Nat.instOne
CategoryTheory.Category.toCategoryStruct
HomologicalComplex.instCategory
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelSemigroup.toIsRightCancelAdd
CategoryTheory.Functor.obj
CochainComplex.singleā‚€
CategoryTheory.InjectiveResolution.cocomplex
CategoryTheory.InjectiveResolution.ι
hom
CategoryTheory.Functor.map
—AddRightCancelSemigroup.toIsRightCancelAdd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
ι_comp_hom
ι_f_zero_comp_hom_f_zero šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
HomologicalComplex.X
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
CategoryTheory.Functor.obj
CochainComplex
HomologicalComplex.instCategory
CochainComplex.singleā‚€
CategoryTheory.InjectiveResolution.cocomplex
HomologicalComplex.Hom.f
CategoryTheory.InjectiveResolution.ι
hom
CategoryTheory.Functor.map
——
ι_f_zero_comp_hom_f_zero_assoc šŸ“–mathematical—CategoryTheory.CategoryStruct.comp
CategoryTheory.Category.toCategoryStruct
HomologicalComplex.X
ComplexShape.up
AddSemigroup.toAdd
AddRightCancelSemigroup.toAddSemigroup
AddRightCancelMonoid.toAddRightCancelSemigroup
AddCancelMonoid.toAddRightCancelMonoid
AddCancelCommMonoid.toAddCancelMonoid
Nat.instAddCancelCommMonoid
AddRightCancelSemigroup.toIsRightCancelAdd
Nat.instOne
CategoryTheory.Functor.obj
CochainComplex
HomologicalComplex.instCategory
CochainComplex.singleā‚€
CategoryTheory.InjectiveResolution.cocomplex
HomologicalComplex.Hom.f
CategoryTheory.InjectiveResolution.ι
hom
CategoryTheory.Functor.map
—AddRightCancelSemigroup.toIsRightCancelAdd
CategoryTheory.Category.assoc
Mathlib.Tactic.Reassoc.eq_whisker'
ι_f_zero_comp_hom_f_zero

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