A restriction category is an abstract formulation for a category of partial maps, defined in terms of certain specified idempotents called the restriction idempotents. All categories of partial maps are restriction categories; conversely, a restriction category is a category of partial maps if and only if the restriction idempotents split. Restriction categories facilitate reasoning about parti...

Among the many possible ways to construct a category equivalent to Boardman’s stable category, the approach of Lewis and May [5] is very convenient for point set analysis of spectra. Their category S of spectra has good formal properties before passage to the stable category and it arises from an easily understood category of prespectra P . In contrast to other categories of spectra, limit and ...

In this paper we study the structure of finitely presented Heyting algebras. Using algebraic techniques (as opposed to techniques from proof-theory) we show that every such Heyting algebra is in fact coHeyting, improving on a result of Ghilardi who showed that Heyting algebras free on a finite set of generators are co-Heyting. Along the way we give a new and simple proof of the finite model pro...

We construct a powerdomain in a category whose objects are posets of data equipped with a cpo of \intensional" representations of the data, and whose morphisms are those monotonic functions between posets that are \realized" by continuous functions between the associated cpos. The category of cpos is contained as a full subcategory that is preserved by lifting, sums, products and function space...

Cofiltered diagrams of spectra, also called pro-spectra, have arisen in diverse areas, and to date have been treated in an ad hoc manner. The purpose of this paper is to systematically develop a homotopy theory of pro-spectra and to study its relation to the usual homotopy theory of spectra, as a foundation for future applications. The surprising result we find is that our homotopy theory of pr...

This paper investigates the Witt groups of triangulated categories of sheaves (of modules over a ring R in which 2 is invertible) equipped with Poincare-Verdier duality. We consider two main cases, that of perfect complexes of sheaves on locally compact Hausdorff spaces and that of cohomologically constructible complexes of sheaves on polyhedra. We show that the Witt groups of the latter form a...

to the morphism f ·p−1, is a bijection provided that X and Y are locally fibrant in the sense that all of their stalks are Kan complexes. Here, π(Z, Y ) denotes simplicial homotopy classes of maps, and the colimit is indexed over homotopy classes represented by hypercovers p : Z → X. A hypercover is a map which is a trivial fibration of simplicial sets in all stalks, and is therefore invertible...

Based on the well-known theory of high-level replacement systems { a categorical formulation of graph grammars { we present new results concerning reenement of high-level replacement systems. Motivated by Petri nets, where reenement is often given by morphisms, we give a categorical notion of reenement. This concept is called Q-transformations and is established within the framework of high-lev...

Based on the well-known theory of high-level replacement systems { a categorical formulation of graph grammars { we present new results concerning reenement of high-level replacement systems. Motivated by Petri nets, where reenement is often given by morphisms, we give a categorical notion of reenement. This concept is called Q-transformations and is established within the framework of high-lev...

A restriction category is an abstract formulation for a category of partial maps, defined in terms of certain specified idempotents called the restriction idempotents. All categories of partial maps are restriction categories; conversely, a restriction category is a category of partial maps if and only if the restriction idempotents split. Restriction categories facilitate reasoning about parti...