In the usual theory of categories, with any two objects A, B of a category A there is associated a set A (A B) of morphisms of A into B. Frequently the set A (A B) is endowed with an additional structure such as a privileged element or an abelian group structure. It has become clear that as the ramifications of the theory of categories increase, the structures that A (A B) will carry will be richer and more complex. The need for a general theory has been widely felt for some time, and beginnings have been made in various directions and often under restrictive hypotheses; e.g. by Mac Lane , Kelly , Bénabou , Linton 
KeywordsCoherence Posite Kelly
Unable to display preview. Download preview PDF.
- Birkhoff, G., and Mac Lane, S., Algebra. Macmillan (1967) (to appear).Google Scholar
- Lawvere, F. W., Functorial semantics of algebraic theories. (Dissertation, Columbia Univ., 1963).Google Scholar
- — Autonomous equational categories. J. Math. Mech. (to appear).Google Scholar