hasPushouts_opposite — Mathlib

English

If C has pullbacks, then Opposite C has pushouts.

Русский

Если в C существуют pullbacks, то в противоположной категории есть pushouts.

LaTeX

$$$${\text{HasPushouts}(C^{\mathrm{op}}) \,=\, \text{HasPullbacks}(C)}.$$$$

Lean4

instance hasPushouts_opposite [HasPullbacks C] : HasPushouts Cᵒᵖ :=
  by
  haveI : HasLimitsOfShape WalkingSpanᵒᵖ C := hasLimitsOfShape_of_equivalence walkingSpanOpEquiv.symm
  infer_instance

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