Theorems · Definition · category theory

CategoryTheory.Over.sections

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    [inst_1 : CategoryTheory.CartesianMonoidalCategory C] →
      (I : C) →
        [inst_2 : CategoryTheory.Closed I] →
          [CategoryTheory.ChosenPullbacksAlong (CategoryTheory.curryRightUnitorHom I)] →
            CategoryTheory.Functor (CategoryTheory.Over I) C

The functor mapping an object X : Over I to the object of sections of X over I, defined by the following pullback diagram. The functor's mapping of morphisms is induced by pullbackMap, that is by the universal property of chosen pullbacks. `` sections X --> I ⟹ X | | | | v v 𝟙_ C --> I ⟹ I ``

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.Sections

Cited by

6 results in Mathlib

Foundations

Depth 38 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.ClosedCategoryTheory.ChosenPullbacksAlong