nLab
arrow category

Contents

Definition

For CC any category, its arrow category is the functor category

Arr(C):=Funct(I,C) Arr(C) := Funct(I,C)

for II the interval category {01}\{0 \to 1\}. Arr(C)Arr(C) is also written [2,C][\mathbf{2},C] or C 2C^{\mathbf{2}} or C Δ[1]C^{\Delta[1]}, since 2 and Δ[1]\Delta[1] (the 1-simplex) etc. are common notation for the interval category.

This means that the objects of Arr(C)Arr(C) are the morphisms (the “arrows”, therefore the name) of CC, while the morphisms of Arr(C)Arr(C) are pairs of CC morphisms constituting commuting square diagrams in CC.

Properties

Revised on March 21, 2013 09:13:06 by Chris Waggoner? (107.205.138.70)