Component Functors

Copower functors

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...

Modular Functors

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

Webster’s Functors

We start with a warm-up: we explain Nakajima’s construction of the geometric sl2-action on ⊕ v Hmid(T ∗Gr(v, w)). 1.1. Warm-up: Nakajima’s geometric action. The lagrangian subvariety φ−1(0) ⊂ M(v) is easily seen to be the zero section Gr(v, w) ⊂ T ∗Gr(v, w). Indeed, consider the action of C× on M(v) induced from the C×-action on T ∗R by fiberwise dilations. Under the identification ofM(v) with ...

Stratifications and Mackey Functors Ii: Globally Defined Mackey Functors

We describe structural properties of globally defined Mackey functors related to the stratification theory of algebras. We show that over a field of characteristic zero they form a highest weight category and we also determine precisely when this category is semisimple. This approach is used to show that the Cartan matrix is often symmetric and non-singular, and we are able to compute finite pa...

Derived Functors