The construction of topological index maps for equivariant families of Dirac operators requires factoring a general smooth map through maps of a very simple type: zero sections of vector bundles, open embeddings, and vector bundle projections. Roughly speaking, a normally non-singular map is a map together with such a factorisation. These factorisations are models for the topological index map....

Let Λ be a radical-square zero algebra over an algebraically closed field k with radical r and Γ = Λ/r 0 r Λ/r ! be the associated hereditary algebra. There is a well-known functor F : modΛ→modΓ which induces a stable equivalence. We show that the functor F keeps Gabriel-Roiter measures and Gabriel-Roiter factors. Thus one may study the Gabriel-Roiter measure for Λ using F and known facts for h...

In order to define a geometric Fourier transform, one usually works with either `-adic sheaves in characteristic p > 0 or with D-modules in characteristic 0. If one considers `-adic sheaves on the stack quotient of a vector bundle V by the homothety action of Gm, however, Laumon provides a uniform geometric construction of the Fourier transform in any characteristic. The category of sheaves on ...

The Eilenberg-Moore constructions and a Beck-type theorem for pairs of monads are described. More specifically, a notion of a Morita context comprising of two monads, two bialgebra functors and two connecting maps is introduced. It is shown that in many cases equivalences between categories of algebras are induced by such Morita contexts. The Eilenberg-Moore category of representations of a Mor...

Recent progress on defining abstract trace semantics for coalgebras rests upon two observations: (i) coalgebraic bisimulation for deterministic automata coincides with trace equivalence, and (ii) the classical powerset construction for automata determinization instantiates the generic idea of lifting a functor to the Eilenberg-Moore category of an appropriate monad T. We take this approach one ...

We show that the Calabi-Yau dimension of the stable module category of a selfinjective algebra of finite representation type is determined by the action of the Nakayama and suspension functors on objects. Our arguments are based on recent results of C. Amiot, and hence apply more generally to triangulated categories having only finitely many indecomposable objects. Throughout, k is an algebraic...

There are several ways to construct omega-categories from combinatorial objects such as pasting schemes or parity complexes. We make these constructions into a functor on a category of chain complexes with additional structure, which we call augmented directed complexes. This functor from augmented directed complexes to omega-categories has a left adjoint, and the adjunction restricts to an equ...

For a certain class of extensions e : 0 → B → E → A → 0 of C∗-algebras in which B and A belong to classifiable classes of C∗-algebras, we show that the functor which sends e to its associated six term exact sequence in K-theory and the positive cones of K0(B) and K0(A) is a classification functor. We give two independent applications addressing the classification of a class of C∗-algebras arisi...

We give a denotational semantics to a calculus with overloading and subtyping. In , the interaction between overloading and subtyping causes self application, and non-normalizing terms exist for each type. Moreover, the semantics of a type depends not on that type alone, but also on in nitely many others. Thus, we need to consider in nitely many domains which are related by an in nite number of...

Abstract. For a split reductive group scheme Ǧ over a commutative ring k with Weyl group W , there is an important functor Rep(Ǧ, k) → Rep(W, k) defined by taking the zero weight space. We prove that the restriction of this functor to the subcategory of small representations has an alternative geometric description, in terms of the affine Grassmannian and the nilpotent cone of the Langlands dua...