Theorems · Theorem · category theory

CategoryTheory.ChosenPullbacksAlong.unit_pullbackId_hom_app

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] (X : C)
  [inst_1 : CategoryTheory.ChosenPullbacksAlong (CategoryTheory.CategoryStruct.id X)] (Y : CategoryTheory.Over X),
  CategoryTheory.CategoryStruct.comp
      ((CategoryTheory.ChosenPullbacksAlong.mapPullbackAdj (CategoryTheory.CategoryStruct.id X)).unit.app Y)
      ((CategoryTheory.ChosenPullbacksAlong.pullbackId X).hom.app
        ((CategoryTheory.Over.map (CategoryTheory.CategoryStruct.id X)).obj Y)) =
    (CategoryTheory.ChosenPullbacksAlong.mapPullbackAdj (CategoryTheory.CategoryStruct.id X)).unit.app Y

Defined in

Mathlib.CategoryTheory.LocallyCartesianClosed.ChosenPullbacksAlong

Cited by

1 results in Mathlib

Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.ChosenPullbacksAlong