Theorems · Definition · category theory
CategoryTheory.MonoOver.mkArrowIso
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X : C} → (f : CategoryTheory.MonoOver X) → CategoryTheory.MonoOver.mk f.arrow ≅ fIf f : MonoOver X, then mk' f.arrow is of course just f, but not definitionally, so we
package it as an isomorphism.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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
- CategoryTheory.Isostatement · cited by 3,963
- CategoryTheory.ObjectProperty.FullSubcategory.objstatement and proof · cited by 1,316
- CategoryTheory.Overstatement · cited by 935
- CategoryTheory.Iso.reflproof · cited by 727
- CategoryTheory.Over.leftstatement and proof · cited by 541
- CategoryTheory.MonoOverstatement and proof · cited by 115
- CategoryTheory.Over.isMonostatement · cited by 111
- CategoryTheory.MonoOver.arrowstatement and proof · cited by 41
- CategoryTheory.MonoOver.mkstatement and proof · cited by 33
- CategoryTheory.MonoOver.isoMkproof · cited by 9
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.MonoOver.mkArrowIso_hom_hom_leftstatement and proof · cited by 0
- CategoryTheory.MonoOver.mkArrowIso_inv_hom_leftstatement and proof · cited by 0