Theorems · Theorem · category theory
CategoryTheory.kernel_zero_of_nonzero_from_simple
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C}
[CategoryTheory.Simple X] {f : X ⟶ Y} [inst_3 : CategoryTheory.Limits.HasKernel f],
f ≠ 0 → CategoryTheory.Limits.kernel.ι f = 0- Defined in
- Mathlib.CategoryTheory.Simple
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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.IsIsoproof · cited by 1,156
- CategoryTheory.Limits.kernelstatement · cited by 272
- CategoryTheory.Limits.kernel.ιstatement and proof · cited by 214
- CategoryTheory.Limits.HasKernelstatement and proof · cited by 169
- CategoryTheory.Simplestatement and proof · cited by 39
- CategoryTheory.isIso_of_mono_of_nonzeroproof · cited by 5
- CategoryTheory.Limits.eq_zero_of_epi_kernelproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- CategoryTheory.mono_of_nonzero_from_simpleproof · cited by 0