Theorems · Theorem · category theory

CategoryTheory.Limits.weakKernel.condition

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {X Y : C} (f : X ⟶ Y) [inst_2 : CategoryTheory.Limits.HasWeakKernel f],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.weakKernel.ι f) f = 0

Defined in: Mathlib.CategoryTheory.Limits.WeakLimits.WeakKernels
Cited by: 1 results in Mathlib
Foundations: Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasWeakKernel

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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.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.parallelPairproof · cited by 766
CategoryTheory.Limits.weakLimit.coneproof · cited by 10
CategoryTheory.Limits.HasWeakKernelstatement and proof · cited by 8
CategoryTheory.Limits.KernelFork.conditionproof · cited by 7
CategoryTheory.Limits.weakKernelstatement · cited by 5
CategoryTheory.Limits.weakKernel.ιstatement · cited by 5

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.weakKernelIsWeakKernelstatement · cited by 1
CategoryTheory.Limits.weakKernel.condition_assocproof · cited by 0