Theorems · Inductive type · category theory

CategoryTheory.Grothendieck

{C : Type u} → [inst : CategoryTheory.Category.{v, u} C] → CategoryTheory.Functor C CategoryTheory.Cat → Type (max u u₂)

The Grothendieck construction (often written as ∫ F in mathematics) for a functor F : C ⥤ Cat gives a category whose * objects X consist of X.base : C and X.fiber : F.obj base * morphisms f : X ⟶ Y consist of base : X.base ⟶ Y.base and f.fiber : (F.map base).obj X.fiber ⟶ Y.fiber

Defined in

Mathlib.CategoryTheory.Grothendieck

Cited by

138 results in Mathlib

Foundations

Depth 32 from the axioms, rests on 169 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category