Theorems · Definition · category theory

CategoryTheory.Limits.spanCompIso

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) →
          {X Y Z : C} →
            (f : X ⟶ Y) →
              (g : X ⟶ Z) → (CategoryTheory.Limits.span f g).comp F ≅ CategoryTheory.Limits.span (F.map f) (F.map g)

A functor applied to a span is a span.

Defined in

Mathlib.CategoryTheory.Limits.Shapes.Pullback.Cospan

Cited by

13 results in Mathlib

Foundations

Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category