pasteHorizIsPushoutEquiv — Mathlib

English

If epi f, then the two legs in a pushout cocone are equal: inl = inr.

Русский

Если epi f, то две стрелки inl и inr в пушпоуте совпадают.

LaTeX

$$$t.inl = t.inr$ for $t$ a PushoutCocone f f with epi f$$

Lean4

/-- Given that the left square is a pushout, the pasted square is a pushout iff the right square is.
-/
def pasteHorizIsPushoutEquiv (H : IsColimit t₁) : IsColimit (t₁.pasteHoriz t₂ hi₂) ≃ IsColimit t₂
    where
  toFun H' := rightSquareIsPushout t₂ _ H H'
  invFun H' := pasteHorizIsPushout _ H H'
  left_inv _ := Subsingleton.elim _ _
  right_inv _ := Subsingleton.elim _ _

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