Theorems · Theorem · category theory

CategoryTheory.Abelian.Pseudoelement.apply_eq_zero_of_comp_eq_zero

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {P Q R : C} (f : Q ⟶ R)
  (a : P ⟶ Q),
  CategoryTheory.CategoryStruct.comp a f = 0 →
    CategoryTheory.Abelian.Pseudoelement.pseudoApply f
        (Quot.mk (CategoryTheory.Abelian.PseudoEqual Q) (CategoryTheory.Over.mk a)) =
      0

Defined in: Mathlib.CategoryTheory.Abelian.Pseudoelements
Cited by: 1 results in Mathlib
Foundations: Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Abelian

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Cites11

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
Quiver.Homstatement and proof · cited by 32,603
CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
CategoryTheory.Abelianstatement and proof · cited by 1,753
CategoryTheory.Overstatement · cited by 935
CategoryTheory.Over.mkstatement and proof · cited by 203
CategoryTheory.Abelian.Pseudoelementstatement · cited by 21
CategoryTheory.Abelian.Pseudoelement.pseudoApplystatement · cited by 18
CategoryTheory.Abelian.Pseudoelement.setoidproof · cited by 16
CategoryTheory.Abelian.PseudoEqualstatement · cited by 12
CategoryTheory.Abelian.Pseudoelement.zero_eq_zeroproof · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.Abelian.Pseudoelement.exact_of_pseudo_exactproof · cited by 0