CATEGORY THEORY 1991 - Clarification of dates The conference will be held JUNE 23-30, 1991, as first announced. Subject: An answer, after 11 weeks absence From: "Fred E.J. Linton" <FLINTON@Wesleyan.bitnet> To: inhb@musicb.mcgill.ca Mike, On the very day I arrived in Iceland for the Jonsson symposium, you asked me: This sounds like something you would have done. If B is a category with a triple T and if K is the Kleisli category, then the category of T-algebras can be identified as the full subcategory of Func(K\op,Set) consisting of all functors R:K\op --> Set such that R o F\op: B\op --> Set is representable. Can you give me a reference? If I had SLN 80 around, I would expect to find it there, but it is easier to ask you. Now that I'm back, I can answer: yep, that's what I did, more or less: but not quite as you say -- that is, not literally the full subcategory you say, but rather the pairs consisting of such functors as one entry and a matching representing object as the other. Done first in the La Jolla volume, but just over Sets , then in SLN 80 in the very first article (An outline of functorial semantics, pp. 7-52), where I wrote A where you write B , and finally, for the "relative category" setting, in a preprint published by the Banach Center in Warsaw in 1974 entitled Relative Functorial Semantics, III: Triples vs. Theories (three whole pages), where I used S (suggesting Sets ) as the notation for the closed, or monoidal, or more generally just multilinear base category relatiove to which all the relative category theory was to be done. OK? -- Fred