Theorems · Theorem · category theory
CategoryTheory.cokernel_zero_of_nonzero_to_simple
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Abelian C] {X Y : C}
[CategoryTheory.Simple Y] {f : X ⟶ Y}, f ≠ 0 → CategoryTheory.Limits.cokernel.π f = 0- Defined in
- Mathlib.CategoryTheory.Simple
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
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.Abelianstatement and proof · cited by 1,753
- CategoryTheory.IsIsoproof · cited by 1,156
- CategoryTheory.Limits.cokernelstatement · cited by 229
- CategoryTheory.Limits.cokernel.πstatement and proof · cited by 194
- CategoryTheory.Simplestatement and proof · cited by 39
- CategoryTheory.isIso_of_epi_of_nonzeroproof · cited by 2
- CategoryTheory.Limits.eq_zero_of_mono_cokernelproof · cited by 2
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