Mathlib Map

Theorems · Definition · category theory

HomologicalComplex.Hom.f

{ι : Type u_1} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] →
        {c : ComplexShape ι} → {A B : HomologicalComplex V c} → A.Hom B → (i : ι) → A.X i ⟶ B.X i
Defined in
Mathlib.Algebra.Homology.HomologicalComplex
Cited by
845 results in Mathlib
Foundations
Depth 4 from the axioms, rests on 12 definitions · uses no axioms
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

CategoryTheory.Functor.mapHomologicalComplex · cited by 145Functor.mapHomologicalCom…CochainComplex.HomComplex.Cochain.ofHom · cited by 121Cochain.ofHomAlgebraicTopology.DoldKan.PInfty · cited by 94DoldKan.PInftyHomologicalComplex.hom_ext · cited by 92HomologicalComplex.hom_extHomologicalComplex.eval · cited by 84HomologicalComplex.evalCochainComplex.shiftFunctor · cited by 50CochainComplex.shiftFunct…CochainComplex.HomComplex.Cochain.ofHom_v · cited by 46Cochain.ofHom_vHomologicalComplex.shortComplexFunctor' · cited by 42HomologicalComplex.shortC…CategoryTheory.Functor.mapBifunctorHomologicalComplex · cited by 35Functor.mapBifunctorHomol…HomologicalComplex.opFunctor · cited by 34HomologicalComplex.opFunc…HomologicalComplex.Hom.comm · cited by 29Hom.commHomologicalComplex₂.flip · cited by 20HomologicalComplex₂.flipHomologicalComplex₂.d₁ · cited by 18HomologicalComplex₂.d₁HomologicalComplex.restrictionMap · cited by 16HomologicalComplex.restri…CategoryTheory.SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁ · cited by 16Splitting.toKaroubiNondeg…CategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsHomologicalComplex.X · cited by 1839HomologicalComplex.XHomologicalComplex · cited by 1691HomologicalComplexComplexShape · cited by 1684ComplexShapeHomologicalComplex.Hom · cited by 23HomologicalComplex.HomHom.fCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by953

Results whose statement or proof uses this declaration.

Showing the 200 most cited of 953.