Sheaf representation of monoidal categories

On Representation Rings in the Context of Monoidal Categories

Autonomization of Monoidal Categories

We define the free autonomous category generated by a monoidal category and study some of its properties. From a linguistic perspective, this expands the range of possible models of meaning within the distributional compositional framework, by allowing nonlinearities in maps. From a categorical point of view, this provides a factorization of the construction in [Preller and Lambek, 2007] of the...

Monoidal Model Categories

A monoidal model category is a model category with a closed monoidal structure which is compatible with the model structure. Given a monoidal model category, we consider the homotopy theory of modules over a given monoid and the homotopy theory of monoids. We make minimal assumptions on our model categories; our results therefore are more general, yet weaker, than the results of [SS97]. In part...

Traced pre-monoidal categories

Motivated by some examples from functional programming, we propose a generalisation of the notion of trace to symmetric premonoidal categories and of Conway operators to Freyd categories. We show that, in a Freyd category, these notions are equivalent, generalising a well-known theorem of Hasegawa and Hyland.

Monoidal categories and multiextensions

We associate to a group-like monoidal groupoid C a principal bundle E satisfying most of the axioms defining a biextension. The obstruction to the existence of a genuine biextension structure on E is exhibited. When this obstruction vanishes, the biextension E is alternating, and a trivialization of E induces a trivialization of C. The analogous theory for monoidal n-categories is also examined...