Theorems · Theorem · category theory
HomologicalComplex.homotopyCofiber.inrX_sndX_assoc
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C] {ι : Type u_2}
{c : ComplexShape ι} {F G : HomologicalComplex C c} (φ : F ⟶ G) [inst_2 : HomologicalComplex.HasHomotopyCofiber φ]
[inst_3 : DecidableRel c.Rel] (i : ι) {Z : C} (h : G.X i ⟶ Z),
CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.inrX φ i)
(CategoryTheory.CategoryStruct.comp (HomologicalComplex.homotopyCofiber.sndX φ i) h) =
h- Defined in
- Mathlib.Algebra.Homology.HomotopyCofiber
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.Category.id_compproof · cited by 1,998
- HomologicalComplex.Xstatement and proof · cited by 1,839
- HomologicalComplexstatement and proof · cited by 1,691
- ComplexShapestatement and proof · cited by 1,684
- ComplexShape.Relstatement and proof · cited by 518
- HomologicalComplex.HasHomotopyCofiberstatement and proof · cited by 225
- HomologicalComplex.homotopyCofiber.Xstatement · cited by 59
Cited by4
Results whose statement or proof uses this declaration.
- HomologicalComplex.homotopyCofiber.inrX_desc_fproof · cited by 4
- HomologicalComplex.homotopyCofiber.inrX_dproof · cited by 1
- HomologicalComplex.cylinder.πCompι₀Homotopy.inrX_nullHomotopy_fproof · cited by 1
- HomologicalComplex.homotopyCofiber.mapArrowHom_compproof · cited by 1