Theorems · Definition · category theory
CategoryTheory.RegularEpi.unop
{C : Type u₁} →
[inst : CategoryTheory.Category.{v₁, u₁} C] →
{X Y : Cᵒᵖ} → {f : X ⟶ Y} → CategoryTheory.RegularEpi f → CategoryTheory.RegularMono f.unopA regular epimorphism in Cᵒᵖ induces a regular monomorphism in C.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 39 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 and proof · cited by 8,081
- Opposite.unopstatement and proof · cited by 2,231
- Quiver.Hom.unopstatement and proof · cited by 903
- CategoryTheory.RegularEpistatement and proof · cited by 16
- CategoryTheory.RegularMonostatement · cited by 14
- CategoryTheory.RegularEpi.leftproof · cited by 4
- CategoryTheory.RegularEpi.rightproof · cited by 4
- CategoryTheory.RegularEpi.Wproof · cited by 3
- CategoryTheory.RegularEpi.isColimitproof · cited by 3
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