  We provide a treatment of isomorphism within a set-theoretic formulation of
dependent type theory. Type expressions are assigned their natural
set-theoretic compositional meaning. Types are divided into small and large
types --- sets and proper classes respectively. Each proper class, such as
"group" or "topological space", has an associated notion of isomorphism in
correspondence with standard definitions. Isomorphism is handled by definging a
groupoid structure on the space of all definable values. The values are
simultaneously objects (oids) and morphism --- they are "morphoids". Soundness
can then be proved for simple and natural inference rules deriving isomorphisms
and for the substitution of isomorphics.
