Theorems · Theorem · category theory
CategoryTheory.MorphismProperty.nonempty_kernels
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
(W : CategoryTheory.MorphismProperty C) {X₁ X₂ : C} (f : X₁ ⟶ X₂),
W f → ∀ [CategoryTheory.Limits.HasKernel f], W.kernels.Nonempty- Cited by
- 0 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
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.MorphismPropertystatement and proof · cited by 2,179
- CategoryTheory.Limits.comp_zeroproof · cited by 365
- CategoryTheory.Limits.kernel.ιproof · cited by 214
- CategoryTheory.Limits.HasKernelstatement and proof · cited by 169
- CategoryTheory.Limits.Fork.ofιproof · cited by 66
- CategoryTheory.Limits.kernel.conditionproof · cited by 52
- CategoryTheory.Limits.kernelIsKernelproof · cited by 24
- CategoryTheory.ObjectProperty.Nonemptystatement · cited by 13
- CategoryTheory.ObjectProperty.nonempty_of_propproof · cited by 5
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