Extending Pirashvili’s work, we characterize small additive categories A such that the inclusion in the category of functors from A to abelian groups of the full subcategory of analytic functors induces an isomorphism between extension groups.

Accessible set functors can be presented by signatures and equations as quotients of polynomial functors. We determine how preservation of pullbacks and other related properties (often applied in coalgebra) are re ected in the structure of the system of equations.

Given a group G, we prove that the 2-category of small categories with G-action and G-equivariant functors is 2-equivalent to the 2-category of small Ggraded categories and degree-preserving functors.

We prove that any endofunctor on a class-theoretic category has a final coalgebra. Moreover, we characterize functors on set-theoretic categories which are identical on objects, and functors which are constant on objects.

We examine the cokernel of canonical homomorphism from trivial source ring a finite group to $p$-rational complex characters. use Boltje and Co\c{s}kun's theory fibered biset functors determine structure cokernel. An essential tool in determination this is Bouc's rational $p$-biset functors.

Recognizable graph languages are a generalization of regular (word) languages to graphs (as well as arbitrary categories). Recently automaton functors were proposed as acceptors of recognizable graph languages. They promise to be a useful tool for the verification of dynamic systems, for example for invariant checking. Since automaton functors may contain an infinite number of finite state sets...

We give a common generalization of two earlier constructions in [2], that yielded coalgebraic type functors for weighted, resp. fuzzy transition systems. Transition labels for these systems were drawn from a commutative monoid M or a complete semilattice L, with the transition structure interacting with the algebraic structure on the labels. Here, we show that those earlier signature functors a...

We prove in this paper that the genus zero data of a modular functor determines the modular functor. We do this by establishing that the S-matrix in genus onewith one point labeled arbitrarily can be expressed in terms of the genus zero information and we give an explicit formula. We do not assume the modular functor in question has duality or is unitary, in order to establish this. CONTENTS