Theorems · Theorem · category theory

HomologicalComplex.restrictionHomologyIso.congr_simp

∀ {ι : Type u_1} {ι' : Type u_2} {c : ComplexShape ι} {c' : ComplexShape ι'} {C : Type u_3}
  [inst : CategoryTheory.Category.{v_1, u_3} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  (K : HomologicalComplex C c') (e : c.Embedding c') [inst_2 : e.IsRelIff] (i i_1 : ι) (e_i : i = i_1) (j k k_1 : ι)
  (e_k : k = k_1) (hi : c.prev j = i) (hk : c.next j = k) {i' i'_1 : ι'} (e_i' : i' = i'_1) {j' k' k'_1 : ι'}
  (e_k' : k' = k'_1) (hi' : e.f i = i') (hj' : e.f j = j') (hk' : e.f k = k') (hi'' : c'.prev j' = i')
  (hk'' : c'.next j' = k') [inst_3 : K.HasHomology j'] [inst_4 : (K.restriction e).HasHomology j],
  K.restrictionHomologyIso e i j k hi hk hi' hj' hk' hi'' hk'' = K.restrictionHomologyIso e i_1 j k_1 ⋯ ⋯ ⋯ hj' ⋯ ⋯ ⋯

Defined in

Mathlib.Algebra.Homology.Embedding.RestrictionHomology

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsComplexShape.Embedding.IsRelIffHomologicalComplex.HasHomologyHomologicalComplex.HasHomology