arrow_ι — Mathlib

English

If two morphisms g1, g2 : widePushout ... → X agree after postcomposing with all injections ι arrows j and with head arrows, then g1 = g2.

Русский

Если два морфизма g1, g2 из widePushout в X согласованы после композиции с каждым ι arrows j и head arrows, тогда g1 = g2.

LaTeX

$$$\\big(\\forall j:\\, J,\\; ι arrows j \\circ g1 = ι arrows j \\circ g2\\big) \\Rightarrow (head arrows \\circ g1 = head arrows \\circ g2) \\Rightarrow g1 = g2$.$$

Lean4

@[reassoc, simp]
theorem arrow_ι (j : J) : arrows j ≫ ι arrows j = head arrows := by
  apply colimit.w (WidePushoutShape.wideSpan _ _ _) (WidePushoutShape.Hom.init j)

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