Abstract

Monads give us a means to describe algebraic structures abstractly. We might want to know: when can we be sure that the operations for a monad all commute pairwise? When that’s the case, it turns out that the category of algebras for the monad resembles the categories of linear algebra. It would be nice to think that this form of commutativity for a monad should echo commutativity for monoids – but since a category of endofunctors is almost never symmetric monoidal with respect to composition, it doesn’t make immediate sense to ask that a monad, regarded as a monoid object, be commutative. This talk will discuss how the question of commutativity was approached in the 70s by Anders Kock; we will consider an example, also due to Kock, which is related to functional analysis and draws on ideas of Bill Lawvere’s.