  This work is the sequel to Continuous Quivers of Type A (I). In this paper we
define the Auslander-Reiten space of a continuous type $A$ quiver, which
generalizes the Auslander-Reiten quiver of type $A_n$ quivers. We prove that
extensions, kernels, and cokernels of representations of type $A_{\mathbb R}$
can be described by lines and rectangles in a way analogous to representations
of type $A_n$. We provide a similar description for distinguished triangles in
the bounded derived category whose first and third terms are indecomposable.
Furthermore, we provide a complete classification of Auslander-Reiten sequences
in the category of finitely generated representations of $A_{\mathbb R}$. This
is part of a longer work; the other papers in this series are with Kiyoshi
Igusa and Gordana Todorov. The goal of this series is to generalize cluster
categories, clusters, and mutation for type $A_n$ quivers to continuous
versions for type $A_{\mathbb R}$ quivers.
  (Added Section 5 to version 2.)
