hasPushoutVertPaste — Mathlib

English

Inverse coherence identity for the left iso with fst and snd maps in the pasted pullback diagram.

Русский

Когерентное тождество для левого изоморфизма с fst и snd в склеенной конфигурации пуллбеков.

LaTeX

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

Lean4

instance hasPushoutVertPaste : HasPushout (f ≫ f') g :=
  HasColimit.mk
    { cocone := (pushout.cocone f g).pasteVert (pushout.cocone f' (pushout.inl f g)) rfl
      isColimit := pasteVertIsPushout rfl (pushout.isColimit f g) (pushout.isColimit f' (pushout.inl f g)) }

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