Theorems · Theorem · category theory
CategoryTheory.Functor.isSplitMono_iff
∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D) {X Y : C} (f : Y ⟶ X) [F.Full] [F.Faithful],
CategoryTheory.IsSplitMono (F.map f) ↔ CategoryTheory.IsSplitMono f- Defined in
- Mathlib.CategoryTheory.Functor.EpiMono
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Classical.choice
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.Functor.objstatement · cited by 19,642
- CategoryTheory.Functorstatement and proof · cited by 16,252
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- CategoryTheory.Functor.Fullstatement and proof · cited by 341
- Nonempty.someproof · cited by 340
- CategoryTheory.Functor.Faithfulstatement and proof · cited by 313
- Equiv.toFunproof · cited by 279
- Equiv.invFunproof · cited by 163
- CategoryTheory.IsSplitMonostatement and proof · cited by 33
- CategoryTheory.IsSplitMono.exists_splitMonoproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.Functor.splitMonoCategoryImpOfIsEquivalenceproof · cited by 0