Theorems · Theorem · category theory

CategoryTheory.Abelian.Pseudoelement.pseudoZero_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {P : C}
  (a : CategoryTheory.Over P), Quot.mk (CategoryTheory.Abelian.PseudoEqual P) a = 0 ↔ a.hom = 0

The pseudoelement induced by an arrow is zero precisely when that arrow is zero.

Defined in

Mathlib.CategoryTheory.Abelian.Pseudoelements

Cited by

3 results in Mathlib

Foundations

Depth 92 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Abelian