Theorems · Theorem · category theory

CategoryTheory.Limits.coker.condition

∀ (C : Type u) [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  [inst_2 : CategoryTheory.Limits.HasCokernels C],
  CategoryTheory.CategoryStruct.comp CategoryTheory.Arrow.leftToRight (CategoryTheory.Limits.coker.π C) = 0

Defined in: Mathlib.CategoryTheory.Limits.Shapes.Kernels
Cited by: 1 results in Mathlib
Foundations: Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasZeroMorphisms CategoryTheory.Limits.HasCokernels

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Cites15

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 · cited by 32,603
CategoryTheory.CategoryStruct.compstatement · cited by 17,999
CategoryTheory.Functorstatement · cited by 16,252
CategoryTheory.Limits.HasZeroMorphismsstatement and proof · cited by 3,275
CategoryTheory.Arrowstatement and proof · cited by 713
CategoryTheory.NatTrans.ext'proof · cited by 340
CategoryTheory.Arrow.homproof · cited by 335
CategoryTheory.Limits.cokernel.conditionproof · cited by 50
CategoryTheory.Limits.HasCokernelsstatement and proof · cited by 47
CategoryTheory.Arrow.leftFuncstatement · cited by 37
CategoryTheory.Arrow.rightFuncstatement · cited by 32

Cited by2

Results whose statement or proof uses this declaration.

CategoryTheory.Limits.cokerIsCokernelstatement and proof · cited by 0
CategoryTheory.Limits.coker.condition_assocproof · cited by 0