Theorems · Theorem · category theory
CategoryTheory.preserves_mono_of_preservesLimit
∀ {C : Type u₁} {D : Type u₂} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
(F : CategoryTheory.Functor C D) {X Y : C} (f : X ⟶ Y)
[CategoryTheory.Limits.PreservesLimit (CategoryTheory.Limits.cospan f f) F] [CategoryTheory.Mono f],
CategoryTheory.Mono (F.map f)If F preserves pullbacks, then it preserves monomorphisms.
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- Foundations
- Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound
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