Theorems · Theorem · category theory

CategoryTheory.ShortComplex.Exact.liftFromProjective.congr_simp

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Abelian C]
  {S : CategoryTheory.ShortComplex C} (hS : S.Exact) {P : C} (f f_1 : P ⟶ S.X₂) (e_f : f = f_1)
  [inst_2 : CategoryTheory.Projective P] (hf : CategoryTheory.CategoryStruct.comp f S.g = 0),
  hS.liftFromProjective f hf = hS.liftFromProjective f_1 ⋯

Defined in

Mathlib.Algebra.Homology.ShortComplex.Exact

Cited by

0 results in Mathlib

Foundations

Depth 97 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.AbelianCategoryTheory.Projective