prodComparison_comp — Mathlib

English

If prodComparison is iso, its inverse is natural in the left argument; i.e., inv(prodComparison F A B) whiskered on the right by g equals whiskered right by F.map g.

Русский

Если prodComparison — изоморфизм, то inv_natural естественно в левом аргументе; inv(prodComparison F A B) ⇢ правое взвешивание g = …

LaTeX

$$prodComparison_inv_natural_whiskerRight F A B f [IsIso (prodComparison F A B)]$$

Lean4

theorem prodComparison_comp :
    prodComparison (F ⋙ G) A B = G.map (prodComparison F A B) ≫ prodComparison G (F.obj A) (F.obj B) :=
  by
  unfold prodComparison
  ext <;> simp [← G.map_comp]

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