Theorems · Theorem · category theory

ComplexShape.Embedding.liftExtend.comm

∀ {ι : Type u_1} {ι' : Type u_2} {c : ComplexShape ι} {c' : ComplexShape ι'} {e : c.Embedding c'} {C : Type u_3}
  [inst : CategoryTheory.Category.{v_1, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasZeroObject C] {K : HomologicalComplex C c'} {L : HomologicalComplex C c}
  [inst_3 : e.IsRelIff] (φ : K.restriction e ⟶ L),
  e.HasLift φ →
    ∀ (i' j' : ι'),
      CategoryTheory.CategoryStruct.comp (ComplexShape.Embedding.liftExtend.f φ i') ((L.extend e).d i' j') =
        CategoryTheory.CategoryStruct.comp (K.d i' j') (ComplexShape.Embedding.liftExtend.f φ j')

Defined in

Mathlib.Algebra.Homology.Embedding.HomEquiv

Cited by

1 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroObjectComplexShape.Embedding.IsRelIff