isCofiltered_of_initial — Mathlib

English

There is a natural equivalence between Arrow (Shrink C) and Arrow C.

Русский

Существует естественная эквивалентность между Arrow(Shrink C) и Arrow C.

LaTeX

$$$\\\\operatorname{Arrow}(\\\\operatorname{Shrink} C) \\simeq \\\\operatorname{Arrow}(C)$$$

Lean4

/-- Let `A` and `B` be cofiltered categories, `L : A ⥤ T` be initial and `R : B ⥤ T`. Then, the
comma category `Comma L R` is cofiltered. -/
theorem isCofiltered_of_initial [IsCofiltered A] [IsCofiltered B] [L.Initial] : IsCofiltered (Comma L R) :=
  IsCofiltered.of_equivalence (Comma.opEquiv _ _).symm

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