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 [...

This paper concerns contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a common characteristic of these functors: every such functor assigns the empty set to Mn(C) for n ≥ 3. The proof relies, in part, on the Kochen-Specker Theorem of qu...

For each standard affine data satisfying some condition on the coroots, we define a group functor on the category of all rings which is a subgroup of some group functor R 7→ G(R[t, t−1])o T (R), where G is a Chevalley scheme and T is a torus. This functor is then shown to satisfy the conditions of the five axioms required by [Ti4] to be a ‘minimal’ Kac-Moody group.

HomX denotes the sheaf-Hom functor of OX -complexes: HomX(E,F )(U) := Hom • U (E|U , F |U ) (U ⊂ X open), the restriction map for U ′ ⊂ U being the obvious one. This “dynamic” sheafified version of Hom• has a derived functor RHom•, defined as usual via q-injective resolutions (which always exist!). Similarly, we have a sheaf-theoretic version of ⊗, and its left-derived functor ⊗ = , defined via...

Building on work done by Myra VanInwegen and Elsa Gunter, we encode the dynamic semantics of the Module system of SML in HOL. We extend this to a possible dynamic semantics for a Module system with higher order functors. We relate these two semantics by embeddings and projections and outline how we are using these to state and prove that the new evaluation relations conservatively extend the ol...

We introduce and develop the notion of displayed categories. A displayed category over a category C is equivalent to ‘a category D and functor F : D → C’, but instead of having a single collection of ‘objects of D’ with a map to the objects of C, the objects are given as a family indexed by objects of C, and similarly for the morphisms. This encapsulates a common way of building categories in p...