Theorems · Theorem · category theory

CategoryTheory.Pseudofunctor.Grothendieck.map_map_fiber

∀ {𝒮 : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} 𝒮]
  {F G : CategoryTheory.Pseudofunctor (CategoryTheory.LocallyDiscrete 𝒮) CategoryTheory.Cat} (α : F ⟶ G)
  {a b : F.Grothendieck} (f : a ⟶ b),
  ((CategoryTheory.Pseudofunctor.Grothendieck.map α).map f).fiber =
    CategoryTheory.CategoryStruct.comp ((α.naturality f.base.toLoc).inv.toNatTrans.app a.fiber)
      ((α.app { as := b.base }).toFunctor.map f.fiber)

Defined in

Mathlib.CategoryTheory.Bicategory.Grothendieck

Cited by

0 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category