A preprint of my paper "Algebraic theory of vector-valued integration" is now available at http://arxiv.org/abs/1108.2913 This paper subsumes the content of my talk of the same name at CT2011. An abstract is included below. Your comments are welcome. Regards, Rory Lucyshyn-Wright Abstract: We define a monad M on a category of measurable bornological sets, and we show how this monad gives rise to a theory of vector-valued integration that is related to the notion of Pettis integral. We show that an algebra X of this monad is a bornological locally convex vector space endowed with operations which associate vectors \int f d\mu in X to incoming maps f : T --> X and measures \mu on T. We prove that a Banach space is an M-algebra as soon as it has a Pettis integral for each incoming bounded weakly-measurable function. It follows that all separable Banach spaces, and all reflexive Banach spaces, are M-algebras. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]