Theorems · Theorem · category theory

CategoryTheory.ShortComplex.HomologyData.comm

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S : CategoryTheory.ShortComplex C} (self : S.HomologyData),
  CategoryTheory.CategoryStruct.comp self.left.π (CategoryTheory.CategoryStruct.comp self.iso.hom self.right.ι) =
    CategoryTheory.CategoryStruct.comp self.left.i self.right.p

the pentagon relation expressing the compatibility of the left and right homology data

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

4 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms