Theorems · Theorem · category theory
CategoryTheory.mono_to_simple_zero_of_not_iso
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C}
[CategoryTheory.Simple Y] {f : X ⟶ Y} [CategoryTheory.Mono f], (CategoryTheory.IsIso f → False) → f = 0- Defined in
- Mathlib.CategoryTheory.Simple
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
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.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.IsIsostatement and proof · cited by 1,156
- CategoryTheory.Monostatement and proof · cited by 893
- CategoryTheory.Simplestatement and proof · cited by 39
- CategoryTheory.isIso_of_mono_of_nonzeroproof · cited by 5
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.