Theorems · Theorem · category theory
CategoryTheory.Limits.le_kernelSubobject
∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X Y : C} [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
(f : X ⟶ Y) [inst_2 : CategoryTheory.Limits.HasKernel f] (A : CategoryTheory.Subobject X),
CategoryTheory.CategoryStruct.comp A.arrow f = 0 → A ≤ CategoryTheory.Limits.kernelSubobject f- Defined in
- Mathlib.CategoryTheory.Subobject.Limits
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
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.Functor.objstatement · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
- CategoryTheory.Subobjectstatement and proof · cited by 385
- CategoryTheory.Subobject.underlyingstatement · cited by 211
- CategoryTheory.Subobject.arrowstatement and proof · cited by 175
- CategoryTheory.Limits.HasKernelstatement and proof · cited by 169
- CategoryTheory.Limits.kernel.liftproof · cited by 64
- CategoryTheory.Limits.kernelSubobjectstatement · cited by 58
- CategoryTheory.Limits.kernel.lift_ιproof · cited by 55
Cited by2
Results whose statement or proof uses this declaration.
- CategoryTheory.Limits.kernelSubobject_comp_monoproof · cited by 3
- CategoryTheory.Limits.kernelSubobject_comp_leproof · cited by 2