Theorems · Definition · category theory

CategoryTheory.Functor.isTerminalConst

(C : Type u_1) →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    {D : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        {X : D} →
          CategoryTheory.Limits.IsTerminal X → CategoryTheory.Limits.IsTerminal ((CategoryTheory.Functor.const C).obj X)

The constant functor returning a specific terminal object is indeed terminal.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.IsTerminal

Cited by

8 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category