hasEqualizers_of_hasKernels — Mathlib

English

If there is a kernel for f − g, then a coequalizer for f and g exists.

Русский

Если существует ядро f − g, то существует кое-равнитель для f и g.

LaTeX

$$HasKernel(f - g) ⇒ HasCoequalizer(f, g)$$

Lean4

/-- If a preadditive category has all kernels, then it also has all equalizers. -/
theorem hasEqualizers_of_hasKernels [HasKernels C] : HasEqualizers C :=
  @hasEqualizers_of_hasLimit_parallelPair _ _ fun {_} {_} f g => hasEqualizer_of_hasKernel f g

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