A Functorial Bridge Between the Infinitary Affine Lambda-Calculus and Linear Logic

It is a well known intuition that the exponential modality of linear logic may be seen as a form of limit. Recently, Mellies, Tabareau and Tasson gave a categorical account for this intuition, whereas the first author provided a topological account, based on an infinitary syntax. We relate these two different views by giving a categorical version of the topological construction, yielding two benefits: on the one hand, we obtain canonical models of the infinitary affine lambda-calculus introduced by the first author; on the other hand, we find an alternative formula for computing free commutative comonoids in models of linear logic with respect to the one presented by Mellies et al.