inl_comp_pushoutSymmetry_hom — Mathlib

English

See item 73034 for a statement about pushout descents under a functor; this is a reiteration in a parallel entry.

Русский

См. пункт 73034 для утверждения о натурализации descent в pushout под функором; повторение в параллельной записи.

LaTeX

$$$$ \mathrm{pushoutComparison}(G,f,g) \circ G(\mathrm{pushout.desc}_{f,g}(w)) = \mathrm{pushout.desc}_{Gf,Gg}(\, \ldots \,) $$$$

Lean4

@[reassoc (attr := simp)]
theorem inl_comp_pushoutSymmetry_hom [HasPushout f g] : pushout.inl _ _ ≫ (pushoutSymmetry f g).hom = pushout.inr _ _ :=
  (colimit.isColimit (span f g)).comp_coconePointUniqueUpToIso_hom (PushoutCocone.flipIsColimit (pushoutIsPushout g f))
    _

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