Theorems · Theorem · category theory
CategoryTheory.Abelian.Pseudoelement.zero_apply
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {P : C} (Q : C)
(a : CategoryTheory.Abelian.Pseudoelement P), CategoryTheory.Abelian.Pseudoelement.pseudoApply 0 a = 0The zero morphism maps every pseudoelement to 0.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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 · cited by 32,603
- CategoryTheory.Abelianstatement and proof · cited by 1,753
- CategoryTheory.Overproof · cited by 935
- CategoryTheory.Limits.comp_zeroproof · cited by 365
- CategoryTheory.Over.mkproof · cited by 203
- CategoryTheory.Abelian.Pseudoelementstatement and proof · cited by 21
- CategoryTheory.Abelian.Pseudoelement.pseudoApplystatement and proof · cited by 18
- CategoryTheory.Abelian.Pseudoelement.setoidproof · cited by 16
- CategoryTheory.Abelian.Pseudoelement.zero_eq_zeroproof · cited by 4
- CategoryTheory.Abelian.Pseudoelement.pseudoApply_mk'proof · cited by 2
- CategoryTheory.Abelian.Pseudoelement.pseudoZero_defproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.Pseudoelement.eq_zero_iffproof · cited by 0