On the monadicity of categories with chosen weighted limits

Steve Lack – 21 January 1998

It is well known that categories with a given (small) class of conical limits are monadic over Cat. Here I presented joint work with Max Kelly in which this result is extended to cover weighted limits. One can further extend this to the context of enriched categories, and to deal with large classes of limit; I did not give details of these issues in this talk. Ross Street was amused by a lemma I used involving comma objects.