Identity Morphisms

Category (mathematics) - Examples
... The category Rel consists of all sets, with binary relations as morphisms ... Any class can be viewed as a category whose only morphisms are the identity morphisms ... has the elements of I as objects and only the identity morphisms as morphisms ...

Enriched Category - Definition
... of objects a,b in C, an arrow idaI → C(a,a) in M designating an identity for every object a in C, and an arrow °abcC(b,c)⊗C(a,b) → C(a,c) in M designating a composition for each triple of ... single-point set, etc.), then each C(a,b) is a set whose elements may be thought of as "individual morphisms" of C, while °, now a function, defines how consecutive ... corresponds to one of the two ways of composing three consecutive individual morphisms from a → b → c → d from C(a,b),C(b,c) and C(c,d) ...