ABSTRACT
Among the influential talks at the conference were those given by John Gray on fibered categories, Freyd on stable homotopy, Barr/ Beck on acyclic models and triples, and Eilenberg/Kelly on closed categories. These are a sampling of the ideas started in La Jolla. Max Kelly went on to found a lively school of category theory in Australia; the same year, Eilenberg and John Moore published their influential paper “Adjoint Functors and Triples.” The basic idea in the paper concerns a pair of adjoint functors F: X A and U: A X; think of X as sets, A as groups, and Fx as the free group generated by the set x, while U is the functor that forgets the group structure on the underlying set. This pair of functors determines an endofunctor T = UF on the underlying category X, while the adjunction produces two natural transformations η: I T and µ: T 2 T with certain simple properties.
