Theorems · Definition · category theory

Profinite.Extend.cocone

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    (G : CategoryTheory.Functor Profiniteᵒᵖ C) →
      (S : Profinite) →
        CategoryTheory.Limits.Cocone
          ((CategoryTheory.CostructuredArrow.proj FintypeCat.toProfinite.op (Opposite.op S)).comp
            (FintypeCat.toProfinite.op.comp G))

Given a functor G from Profiniteᵒᵖ and S : Profinite, we obtain a cocone on (CostructuredArrow.proj toProfinite.op ⟨S⟩ ⋙ toProfinite.op ⋙ G) with cocone point G.obj ⟨S⟩. Whiskering this cocone with Profinite.Extend.functorOp c gives G.mapCocone c.op as we check in the example below.

Defined in

Mathlib.Topology.Category.Profinite.Extend

Cited by

5 results in Mathlib

Foundations

Depth 94 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category