Functors which are determined, up to natural isomorphism, by their values on objects, are called DVO (Defined by Values on Objects). We focus on the collection of polynomial functors on a category of sets (classes), and we give a characterization theorem of the DVO functors over such collection of functors. Moreover, we show that the (κ-bounded) powerset functor is not DVO.

Mackey functors are a framework having the common properties of many natural constructions for finite groups, such as group cohomology, representation rings, the Bumside ring, the topological K-theory of classifying spaces, the algebraic K-theory of group rings, the Witt rings of Galois extensions, etc. In this work we first show that the Mackey functors for a group may be identified with the m...

We present a higher-order module discipline with separate compilation and concurrent dynamic linking. Based on first-order modules one can program security policies for systems that link modules from untrusted locations (e.g., Java). We introduce a pickling operation that writes persistent clones of volatile, possibly higher-order data structures on the file system. Our pickling operation respe...

We introduce a new categorical framework for studying derived functors, and in particular for comparing composites of left and right derived functors. Our central observation is that model categories are the objects of a double category whose vertical and horizontal arrows are left and right Quillen functors, respectively, and that passage to derived functors is functorial at the level of this ...

By work of Farinati, Solberg, and Taillefer, it is known that the Hopf algebra cohomology a quasi-triangular algebra, as graded Lie under Gerstenhaber bracket, abelian. Motivated by question whether this holds for nonquasi-triangular algebras, we show brackets on can be expressed via an arbitrary projective resolution using Volkov's homotopy liftings generalized to some exact monoidal categorie...

I will build some standard resolutions for Mackey functors which are projective relative to p-subgroups. Those resolutions are closely related to the poset of p-subgroups. They lead to generalizations of known results on cohomology. They give a way to compute the Cartan matrix for Mackey functors, in terms of p-permutation modules, and to precise the structure of projective Mackey functors. The...

Rhetorical biset functors can be defined for any family of finite groups that is closed under subquotients up to isomorphism. The rhetorical p-biset functors almost coincide with the rational p-biset functors. We show that, over a field with characteristic zero, the rhetorical biset functors are semisimple and, furthermore, they admit a character theory involving primitive characters of automor...