Theorems · Theorem · category theory

CategoryTheory.IsNormalMonoCategory.normalMonoOfMono

∀ {C : Type u₁} {inst : CategoryTheory.Category.{v₁, u₁} C} {inst_1 : CategoryTheory.Limits.HasZeroMorphisms C}
  [self : CategoryTheory.IsNormalMonoCategory C] {X Y : C} (f : X ⟶ Y) [CategoryTheory.Mono f],
  Nonempty (CategoryTheory.NormalMono f)

A normal mono category is a category in which every monomorphism is normal.

Defined in: Mathlib.CategoryTheory.Limits.Shapes.NormalMono.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 3 from the axioms · uses no axioms
Assumes: CategoryTheory.IsNormalMonoCategory CategoryTheory.Mono

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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 · cited by 32,603
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Monostatement · cited by 893
CategoryTheory.IsNormalMonoCategorystatement and proof · cited by 9
CategoryTheory.NormalMonostatement · cited by 4

Cited by1

Results whose statement or proof uses this declaration.

CategoryTheory.normalMonoOfMonoproof · cited by 3