Theorems · Theorem · category theory

HomologicalComplex.image_to_eq_image

∀ {ι : Type u_1} {V : Type u} [inst : CategoryTheory.Category.{v, u} V]
  [inst_1 : CategoryTheory.Limits.HasZeroMorphisms V] {c : ComplexShape ι} (C : HomologicalComplex V c)
  [inst_2 : CategoryTheory.Limits.HasImages V] [CategoryTheory.Limits.HasEqualizers V] {i j : ι},
  c.Rel i j → CategoryTheory.Limits.imageSubobject (C.dTo j) = CategoryTheory.Limits.imageSubobject (C.d i j)

Defined in

Mathlib.Algebra.Homology.HomologicalComplex

Cited by

0 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasImagesCategoryTheory.Limits.HasEqualizers