Theorems · Theorem · category theory

CategoryTheory.Over.sections_map

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.CartesianMonoidalCategory C]
  (I : C) [inst_2 : CategoryTheory.Closed I]
  [inst_3 : CategoryTheory.ChosenPullbacksAlong (CategoryTheory.curryRightUnitorHom I)] {X Y : CategoryTheory.Over I}
  (u : X ⟶ Y),
  (CategoryTheory.Over.sections I).map u =
    CategoryTheory.ChosenPullbacksAlong.pullbackMap ((CategoryTheory.ihom I).map Y.hom)
      (CategoryTheory.curryRightUnitorHom I) ((CategoryTheory.ihom I).map X.hom) (CategoryTheory.curryRightUnitorHom I)
      ((CategoryTheory.ihom I).map (CategoryTheory.Over.Hom.left u))
      (CategoryTheory.CategoryStruct.id (CategoryTheory.MonoidalCategoryStruct.tensorUnit C))
      (CategoryTheory.CategoryStruct.id (I ⟹ I)) ⋯ ⋯

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.Sections

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CartesianMonoidalCategoryCategoryTheory.ClosedCategoryTheory.ChosenPullbacksAlong