Theorems · Definition · category theory

CategoryTheory.Under.forgetMapInitial

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    (X : C) →
      {I : C} →
        (hI : CategoryTheory.Limits.IsInitial I) →
          CategoryTheory.Under.forget X ≅
            (CategoryTheory.Under.map (hI.to X)).comp (CategoryTheory.Under.equivalenceOfIsInitial hI).functor

The category under any object X factors through the category under the initial object I.

Defined in

Mathlib.CategoryTheory.Comma.Over.Pullback

Cited by

2 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category