Theorems · Theorem · category theory
CategoryTheory.RegularMono.w
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {X Y : C} {f : X ⟶ Y} (self : CategoryTheory.RegularMono f),
CategoryTheory.CategoryStruct.comp f self.left = CategoryTheory.CategoryStruct.comp f self.rightf equalizes the two maps
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 5 from the axioms · uses no axioms
- Assumes
- CategoryTheory.Category
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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 and proof · cited by 32,603
- CategoryTheory.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.RegularMonostatement and proof · cited by 14
- CategoryTheory.RegularMono.rightstatement · cited by 3
- CategoryTheory.RegularMono.Zstatement · cited by 3
- CategoryTheory.RegularMono.leftstatement · cited by 3
Cited by7
Results whose statement or proof uses this declaration.
- CategoryTheory.RegularMono.opproof · cited by 2
- CategoryTheory.RegularMono.strongMonoproof · cited by 1
- CategoryTheory.RegularMono.isLimitstatement · cited by 1
- CategoryTheory.RegularMono.ofArrowIsoproof · cited by 0
- CategoryTheory.regularOfIsPullbackSndOfRegularproof · cited by 0
- CategoryTheory.RegularMono.w_assocproof · cited by 0
- CategoryTheory.IsRegularMono.wproof · cited by 0