hasCoequalizers_of_hasCokernels — Mathlib

English

If a preadditive category has all cokernels, then it has all coequalizers.

Русский

В преддобавительной категории, если существуют все кокernelы, существуют все кое-равнители.

LaTeX

$$HasCokernels C ⇒ HasCoequalizers C$$

Lean4

/-- If a preadditive category has all cokernels, then it also has all coequalizers. -/
theorem hasCoequalizers_of_hasCokernels [HasCokernels C] : HasCoequalizers C :=
  @hasCoequalizers_of_hasColimit_parallelPair _ _ fun {_} {_} f g => hasCoequalizer_of_hasCokernel f g

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