Theorems · Definition · category theory

CategoryTheory.StructuredArrow

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} → [inst_1 : CategoryTheory.Category.{v₂, u₂} D] → D → CategoryTheory.Functor C D → Type (max u₁ v₂)

The category of T-structured arrows with domain S : D (here T : C ⥤ D), has as its objects D-morphisms of the form S ⟶ T Y, for some Y : C, and morphisms C-morphisms Y ⟶ Y' making the obvious triangle commute.

Defined in

Mathlib.CategoryTheory.Comma.StructuredArrow.Basic

Cited by

370 results in Mathlib

Foundations

Depth 23 from the axioms, rests on 120 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Category