Theorems · Definition · category theory
CategoryTheory.RegularMono.op
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X Y : C} → {f : X ⟶ Y} → CategoryTheory.RegularMono f → CategoryTheory.RegularEpi f.opA regular monomorphism in C induces a regular epimorphism in Cᵒᵖ.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 40 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- Oppositestatement · cited by 8,081
- Quiver.Hom.opstatement and proof · cited by 1,948
- CategoryTheory.RegularEpistatement · cited by 16
- CategoryTheory.RegularMonostatement and proof · cited by 14
- CategoryTheory.RegularMono.rightproof · cited by 3
- CategoryTheory.RegularMono.wproof · cited by 3
- CategoryTheory.RegularMono.leftproof · cited by 3
- CategoryTheory.RegularMono.Zproof · cited by 3
- CategoryTheory.Limits.Fork.isLimitOfιEquivIsColimitOpproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.isRegularEpi_op_iff_isRegularMonoproof · cited by 1
- CategoryTheory.isRegularMono_unop_iff_isRegularEpiproof · cited by 0