inr_pushoutRightPushoutInlIso_inv

English

A detailed coherence relation for the snd-snd interaction with the left iso in the pasted configuration.

Русский

Детальное когерентное отношение для взаимодействия snd-snd с левым изоморфизмом в конфигурации pasting.

LaTeX

$$$(\\mathrm{pullbackLeftPullbackSndIso}(f,g,g')).inv \\circ (\\mathrm{pullback.snd}(f,g) \\circ \\mathrm{pullback.snd}(\\mathrm{pullback.snd} f g, g')) = \\mathrm{pullback.snd}(f, (\\mathrm{pushout.inl} f g) g')$$$

Lean4

@[reassoc (attr := simp)]
theorem inr_pushoutRightPushoutInlIso_inv :
    pushout.inr _ _ ≫ (pushoutRightPushoutInlIso f g f').inv = pushout.inr _ _ ≫ pushout.inr _ _ :=
  IsColimit.comp_coconePointUniqueUpToIso_inv _ _ WalkingSpan.right

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