Theorems · Theorem · category theory
CategoryTheory.mono_of_nonzero_from_simple
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
[CategoryTheory.Limits.HasKernels C] {X Y : C} [CategoryTheory.Simple X] {f : X ⟶ Y}, f ≠ 0 → CategoryTheory.Mono f- Defined in
- Mathlib.CategoryTheory.Preadditive.Schur
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
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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 and proof · cited by 32,603
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- CategoryTheory.Monostatement · cited by 893
- CategoryTheory.Limits.HasKernelsstatement and proof · cited by 67
- CategoryTheory.Simplestatement and proof · cited by 39
- CategoryTheory.Preadditive.mono_of_kernel_zeroproof · cited by 3
- CategoryTheory.kernel_zero_of_nonzero_from_simpleproof · cited by 1
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