In category theory, if C
and D
are both categories, then a functor from C
to D
maps every morphism in C
to some morphism in D
. You can think of a functor as a set of "morphism-to-morphism"-morphisms. Furthermore, if the functor maps from category C
to category C
(i.e., D=C
), this is called an endofunctor.
In mm-ADT, in the type subgraph of the obj
graph, the vertices denote types and a path (of edges) back to the root of the graph (a ctype root) denotes a type definition. These edges are labeled with instructions from inst
, where a path is a sequence of operations that morph one type into another type (see The Type). In abstract algebra, the type subgraph is called a (generalized) Cayley graph as the obj
graph captures the structure of the underlying inst
monoid. N