Theorems · Theorem · category theory

CategoryTheory.CostructuredArrow.IsUniversal.fac

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {T : D} {S : CategoryTheory.Functor C D} {f : CategoryTheory.CostructuredArrow S T} (h : f.IsUniversal)
  (g : CategoryTheory.CostructuredArrow S T), CategoryTheory.CategoryStruct.comp (S.map (h.lift g)) f.hom = g.hom

Any costructured arrow factors through a universal arrow.

Defined in

Mathlib.CategoryTheory.Comma.StructuredArrow.Basic

Cited by

4 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category