Theorems · Theorem · category theory

CategoryTheory.Limits.KernelFork.IsLimit.isZero_of_mono

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] {X Y : C}
  {f : X ⟶ Y} {c : CategoryTheory.Limits.KernelFork f} (hc : CategoryTheory.Limits.IsLimit c) [CategoryTheory.Mono f],
  CategoryTheory.Limits.IsZero c.pt

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Kernels
Cited by: 3 results in Mathlib
Foundations: Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Mono

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Cites20

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.compproof · cited by 17,999
CategoryTheory.Category.assocproof · cited by 6,433
CategoryTheory.CategoryStruct.idproof · cited by 6,235
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Limits.Cone.ptstatement and proof · cited by 1,298
CategoryTheory.Monostatement and proof · cited by 893
CategoryTheory.Limits.WalkingParallelPairstatement · cited by 781
CategoryTheory.Limits.parallelPairstatement · cited by 766
CategoryTheory.Limits.IsLimitstatement and proof · cited by 664
CategoryTheory.cancel_monoproof · cited by 435

Cited by3

Results whose statement or proof uses this declaration.

CategoryTheory.Abelian.isoModSerre_kernel_eq_inverseImage_isomorphismsproof · cited by 2
CategoryTheory.Limits.isZero_kernel_of_monoproof · cited by 1
CategoryTheory.Preadditive.mono_iff_isZero_kernel'proof · cited by 1