We study the problem of constructing a contragredient functor on the category of admissible locally analytic representations of p-adic analytic group G. A naive contragredient does not exist. As a best approximation, we construct an involutive “duality” functor from the bounded derived category of modules over the distribution algebra of G with coadmissible cohomology to itself. on the subcateg...

For a functor F ⊃ Id on the category of metrizable compacta, we introduce a conception of a linear functorial operator T = {TX : Pc(X) → Pc(FX)} extending (for each X) pseudometrics from X onto FX ⊃ X (briefly LFOEP for F ). The main result states that the functor SP G of G-symmetric power admits a LFOEP if and only if the action of G on {1, . . . , n} has a one-point orbit. Since both the hype...

We define an “algebraic” version of the Goodwillie tower, P alg n F (X), that depends only on the behavior of F on coproducts of X . When F is a functor to connected spaces or grouplike H-spaces, the functor P alg n F is the base of a fibration |⊥ F | → F → P alg n F, whose fiber is the simplicial space associated to a cotriple ⊥ built from the (n + 1) cross effect of the functor F . When the c...

Semi-regular locales are extensions of the classical semiregular spaces. We investigate the conditions such that semi-regularization is a functor. We also investigate the conditions such that semi-regularization is a reflection or coreflection.

We study spectral triples on (weighted) groups and consider functors between the categories of weighted groups and spectral triples. We study the properties of weights and the corresponding functor for spectral triples coming from discrete weighted groups.

Recently, a new category of domains used for the mathematical foundations of denotational semantics, that of L-domains, has been under study. In this paper we consider a related category of posets, that of local lattices. First, a completion operator taking posets to local lattices is developed, and then this operator is extended to a functor from posets with embedding-projection pairs to local...

In order to investigate sheaves on abelian varieties, Mukai [Mu1] introduced a very powerful tool called Fourier-Mukai functor. As an application, Mukai ([Mu1], [Mu4]) computed some moduli spaces of stable sheaves on abelian varieties. Recently, Dekker [D] found some examples of isomorphisms of moduli spaces of sheaves induced by Fourier-Mukai functors. As an application, he proved that moduli ...

In the sequel M is a Petri net. Let us consider X , Y . Let us assume that X misses Y . The functor PTempty f (X ,Y ) yielding a strict Petri net is defined by: (Def. 4)2 PTempty f (X ,Y ) = 〈X ,Y, / 0〉. Let us consider X . The functor Tempty f (X) yields a strict Petri net and is defined by: (Def. 5) Tempty f (X) = PTempty f (X , / 0). The functor Pempty f (X) yields a strict Petri net and is ...

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

The concept of indexing of a category (a part of indexed category, see [14]) is introduced as a pair formed by a many sorted category and a many sorted functor. The indexing of a category C against to [14] is not a functor but it can be treated as a functor from C into some categorial category (see [1]). The goal of the article is to work out the notation necessary to define institutions (see [...