Theorems · Theorem · category theory

CategoryTheory.IsCofiltered.infTo_commutes

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.IsCofiltered C] (O : Finset C)
  (H : Finset ((X : C) ×' (Y : C) ×' (_ : X ∈ O) ×' (_ : Y ∈ O) ×' (X ⟶ Y))) {X Y : C} (mX : X ∈ O) (mY : Y ∈ O)
  {f : X ⟶ Y},
  ⟨X, ⟨Y, ⟨mX, ⟨mY, f⟩⟩⟩⟩ ∈ H →
    CategoryTheory.CategoryStruct.comp (CategoryTheory.IsCofiltered.infTo O H mX) f =
      CategoryTheory.IsCofiltered.infTo O H mY

The triangles consisting of a morphism in H and the maps from inf O H commute.

Defined in

Mathlib.CategoryTheory.Filtered.Basic

Cited by

2 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.IsCofiltered