Theorems · Definition · category theory

CategoryTheory.overEquivOfIsInitial

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [CategoryTheory.Limits.HasStrictInitialObjects C] →
      (X : C) → CategoryTheory.Limits.IsInitial X → (CategoryTheory.Over X ≌ CategoryTheory.Discrete PUnit.{w + 1})

If C has strict initial objects and X is an initial object, the category Over X is equivalent to a point.

Defined in

Mathlib.CategoryTheory.Comma.Over.StrictInitial

Cited by

4 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasStrictInitialObjects