hasEqualizers_of_hasPullbacks_and_binary_products

English

Any category with pullbacks and binary products has equalizers.

Русский

Любая категория с pullbacks и бинарными произведениями имеет равносоздающие (равносиленные) объекты.

LaTeX

$$$[HasPullbacks C] \\land [HasBinaryProducts C] \\Rightarrow HasEqualizers C$$$

Lean4

/-- Any category with pullbacks and binary products, has equalizers. -/
theorem hasEqualizers_of_hasPullbacks_and_binary_products [HasBinaryProducts C] [HasPullbacks C] : HasEqualizers C :=
  {
    has_limit := fun F =>
      HasLimit.mk
        { cone := equalizerCone F
          isLimit := equalizerConeIsLimit F } }

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