Sequential products in effect categories

Abstract: A new categorical framework is provided for dealing with multiple arguments in a programming language with effects, for example in a language with imperative features. Like related frameworks (Monads, Arrows, Freyd categories), we distinguish two kinds of functions. In addition, we also distinguish two kinds of equations. Then, we are able to define a kind of product, that generalizes the usual categorical product. This yields a powerful tool for deriving many results about languages with effects.