Theorems · Theorem · category theory

CategoryTheory.Functor.initial_const_initial

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  [CategoryTheory.IsCofiltered C] [inst_3 : CategoryTheory.Limits.HasInitial D],
  ((CategoryTheory.Functor.const C).obj (⊥_ D)).Initial

The inclusion of the initial object is initial.

Defined in

Mathlib.CategoryTheory.Filtered.Final

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.IsCofilteredCategoryTheory.Limits.HasInitial