In this paper we will try to introduce a good smoothness notion for a functor. We consider properties and conditions from geometry and algebraic geometry which we expect a smooth functor should has.

It appears possible to give a fairly standard denotational semantics for the π-calculus, provided that we work within a functor category indexed by a category I of finite sets and injections. The construction is driven by the expansion law, and resembles Abramsky’s domain of synchronisation trees [1]. It also extends Ingólfsdóttir’s work on domain models of value-passing CCS [4]. The relevant p...

We study algebraic properties of categories of Merotopic, Nearness, and Filter Algebras. We show that the category of filter torsion free abelian groups is an epireflective subcategory of the category of filter abelian groups. The forgetful functor from the category of filter rings to filter monoids is essentially algebraic and the forgetful functor from the category of filter groups to the cat...

We produce a highly structured way of associating a simplicial category to a model category which improves on work of Dwyer and Kan and answers a question of Hovey. We show that model categories satisfying a certain axiom are Quillen equivalent to simplicial model categories. A simplicial model category provides higher order structure such as composable mapping spaces and homotopy colimits. We ...

We study the representation theory of the invariant subalgebra of the Weyl algebra under a torus action, which we call a “hypertoric enveloping algebra.” We define an analogue of BGG category O for this algebra, and identify it with a certain category of sheaves on a hypertoric variety. We prove that a regular block of this category is highest weight and Koszul, identify its Koszul dual, comput...

In this paper, we give three functors $mathfrak{P}$, $[cdot]_K$ and $mathfrak{F}$ on the category of C$^ast$-algebras. The functor $mathfrak{P}$ assigns to each C$^ast$-algebra $mathcal{A}$ a pre-C$^ast$-algebra $mathfrak{P}(mathcal{A})$ with completion $[mathcal{A}]_K$. The functor $[cdot]_K$ assigns to each C$^ast$-algebra $mathcal{A}$ the Cauchy extension $[mathcal{A}]_K$ of $mathcal{A}$ by ...

We study the category O for a general Coxeter system using a formulation of Fiebig. The translation functors, the Zuckerman functors and the twisting functors are defined. We prove the fundamental properties of these functors, the duality of Zuckerman functor and generalization of Verma’s result about homomorphisms between Verma modules.