Dear Friends, For those who don't necessarily check the arXiv over breakfast, or like RSS feeds: I've posted the following on the arXiv "Distributive laws for Lawvere theories" (abstract below). http://arxiv.org/abs/1112.3076 This is the work I presented at CT11 in Vancouver, and also at Louvain-la-Neuve and the Scottish Category Theory seminar in Glasgow earlier in the year. Comments are welcome. Best wishes for surviving the "festive" season, Eugenia --- Eugenia Cheng, Senior Lecturer in Pure Mathematics University of Sheffield http://cheng.staff.shef.ac.uk/ I'm supposed to put the words "Times Higher Education University of the Year" in my tagline, so there they are. Title: Distributive laws for Lawvere theories Authors: Eugenia Cheng Categories: math.CT Comments: 36 pages, presented at CT2011 Distributive laws give a way of combining two algebraic structures expressed as monads; in this paper we propose a theory of distributive laws for combining algebraic structures expressed as Lawvere theories. We propose four approaches, involving profunctors, monoidal profunctors, an extension of the free finite-product category 2-monad from Cat to Prof, and factorisation systems respectively. We exhibit comparison functors between CAT and each of these new frameworks to show that the distributive laws between the Lawvere theories correspond in a suitable way to distributive laws between their associated finitary monads. The different but equivalent formulations then provide, between them, a framework conducive to generalisation, but also an explicit description of the composite theories arising from distributive laws. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]