Theorems · Theorem · category theory
CategoryTheory.Functor.strongMono_map_iff_strongMono_of_isEquivalence
∀ {C : Type u_1} {D : Type u_2} [inst : CategoryTheory.Category.{v_1, u_1} C]
[inst_1 : CategoryTheory.Category.{v_2, u_2} D] {F : CategoryTheory.Functor C D} {A B : C} (f : B ⟶ A)
[F.IsEquivalence], CategoryTheory.StrongMono (F.map f) ↔ CategoryTheory.StrongMono f- Defined in
- Mathlib.CategoryTheory.Functor.EpiMono
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
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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.Isoproof · cited by 3,963
- CategoryTheory.Equivalence.unitIsoproof · cited by 536
- CategoryTheory.Arrow.mkproof · cited by 421
- CategoryTheory.Functor.IsEquivalencestatement and proof · cited by 111
- CategoryTheory.Functor.asEquivalenceproof · cited by 58
- CategoryTheory.Functor.invproof · cited by 27
- CategoryTheory.StrongMonostatement and proof · cited by 11
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