Theorems · Definition · category theory
CategoryTheory.Limits.IsZero.to_
{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → {X : C} → CategoryTheory.Limits.IsZero X → (Y : C) → X ⟶ YIf h : IsZero X, then h.to_ Y is a choice of unique morphism X → Y.
to is a reserved word, it was replaced by to_
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 3 from the axioms · uses Classical.choice
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.Limits.IsZerostatement and proof · cited by 306
Cited by10
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.IsZero.of_isoproof · cited by 35
- CategoryTheory.Limits.IsZero.isoproof · cited by 11
- CategoryTheory.Limits.IsZero.unopproof · cited by 5
- CategoryTheory.Limits.IsZero.opproof · cited by 5
- CategoryTheory.Functor.isZeroproof · cited by 5
- CategoryTheory.Limits.IsZero.eq_tostatement · cited by 2
- CategoryTheory.Limits.IsZero.isIsoproof · cited by 1
- CategoryTheory.Limits.IsZero.retractproof · cited by 1
- CategoryTheory.Limits.IsZero.projectiveproof · cited by 0
- CategoryTheory.Limits.IsZero.to_eqstatement · cited by 0