Mackey functors on compact closed categories.
We prove a number of results involving categories enriched over CMet, the category of complete metric spaces with possibly infinite distances. The category CPMet of path complete metric spaces is locally -presentable, closed monoidal, and coreflective in CMet. We also prove that the category CCMet of convex complete metric spaces is not closed monoidal and characterize the isometry--generated objects in CMet, CPMet and CCMet, answering questions by Di Liberti and Rosický. Other results include...
We introduce the connected sum for modular operads. This gives us a graded commutative associative product, and together with the BV bracket and the BV Laplacian obtained from the operadic composition and self-composition, we construct the full Batalin-Vilkovisky algebra. The BV Laplacian is then used as a perturbation of the special deformation retract of formal functions to construct a minimal model and compute an effective action.
Conditions which imply Morita equivalences of functor categories are described. As an application a Dold-Kan type theorem for functors defined on a category associated to associative algebras with one-side units is proved.