For a semisimple complex Lie algebra g, the BGG category O is of particular interest in representation theory. It known that Irving's shuffling functors Shw, indexed by elements w∈W Weyl group, induce an action braid group BW associated to W on derived categories Db(Oλ) blocks O. We show for maximal parabolic subalgebras p sln corresponding subgroup Wp=Sn−1×S1 Sn, LShsi are instances Seidel and...

Abstract We construct a calculus of functors in the spirit orthogonal calculus, which is designed to study ‘functors with reality’ such as Real classifying space functor, . The produces Taylor tower, n -th layer classified by spectrum an action further give model categorical considerations, producing zigzag Quillen equivalences between spectra and structure on category input captures homotopy t...

We classify various types of graded extensions a finite braided tensor category $$\mathcal {B}$$ in terms its 2-categorical Picard groups. In particular, we prove that by group A correspond to monoidal 2-functors from the (consisting invertible central -module categories). Such functors can be expressed Eilnberg-Mac Lane cohomology. describe detail groups symmetric fusion categories and pointed...

The theory of Whittaker functors for GLn is an essential technical tools in Gaitsgory’s proof of the Vanishing Conjecture appearing in the geometric Langlands correspondence ([5]). We define Whittaker functors for GSp 4 and study their properties. These functors correspond to the maximal parabolic subgroup of GSp 4 , whose unipotent radical is not commutative. We also study similar functors cor...

In this paper it is shown that the product of categories and the product of functors may be extended from the structural to the phenomenological domains. For the phenomenological domains the products of functors applies both to functors and autofunctors. Examples of such products representing feasible physical and informational processes are given in the case of the generation of a phenomenolog...

All Mackey functors over a finite group G are built up by short exact sequences from Mackey functors arising from modules over the integral group rings of appropriate subquotients W H of G. The equivariant cohomology theories with coefficients in Mackey functors arising from W H-modules admit particularly simple descriptions. Let G be a finite group. The notion of a Mackey functor plays a funda...

The quasicategory Q of all set functors (i.e. endofunctors of the category SET of all sets and mappings) and all natural transformations has a terminal object – the constant functor C1. We construct here the terminal (or at least the smallest weakly terminal object, which is rigid) in some important subquasicategories of Q – in the quasicategory F of faithful connected set functors and all natu...

Applicative functors [6] are a generalisation of monads. Both allow the expression of effectful computations into an otherwise pure language, like Haskell [5]. Applicative functors are to be preferred to monads when the structure of a computation is fixed a priori. That makes it possible to perform certain kinds of static analysis on applicative values. We define a notion of free applicative fu...