For a broad collection of categories K, including all presheaf categories, the following statement is proved to be consistent: every left exact (i.e. finite-limits preserving) functor from K to Set is small, that is, a small colimit of representables. In contrast, for the (presheaf) category K = Alg(1, 1) of unary algebras we construct a functor from Alg(1, 1) to Set which preserves finite prod...

1.1. Injective resolutions. Let C be an abelian category. An object I ∈ C is injective if the functor Hom(−, I) is exact. An injective resolution of an object A ∈ C is an exact sequence 0→ A→ I → I → . . . where I• are injective. We say C has enough injectives if every object has an injective resolution. It is easy to see that this is equivalent to saying every object can be embedded in an inje...

We fix a field k. All the schemes we will consider will be separated and of finite type over k. If X is a scheme, we write D c(X) for the category of bounded constructible `-adic complexes on X or, if k = C, for bounded constructible complexes on X(C). (The formalism will work in both cases.) In both cases, we’ll write Perv(X) for the heart of the selfdual perverse tstructure on D c(X). When we...

Finding common motifs from a set of strings coding biological sequences is an important problem in Molecular Biology. Several versions of the motif finding problem have been proposed in the literature and for each version, numerous algorithms have been developed. However, many of these algorithms fall under the category of heuristics. In this paper, we concentrate on the Simple Motif Problem (S...

The study of semi-supervised category learning has shown mixed results on how people jointly use labeled and unlabeled information when learning categories. Here we investigate the possibility that people are sensitive to the value of both labeled and unlabeled items, and that this depends on the structure of the underlying categories. We use an unconstrained free-sorting categorization experim...

We develop the theory of Hopf bimodules for a finite rigid tensor category C. Then we use this theory to define a distinguished invertible object D of C and an isomorphism of tensor functors δ : V ∗∗ → D⊗∗∗V ⊗D. This provides a categorical generalization of Radford’s S formula for finite dimensional Hopf algebras [R1], which was proved in [N] for weak Hopf algebras, in [HN] for quasi-Hopf algeb...

In this paper we present a new scheduling problem and describe a shortest path based heuristic as well as a dynamic programming based exact optimization algorithm to solve it. The Selective Multi-Category Parallel-Servicing Problem (SMCPSP) arises when a set of jobs has to be scheduled on a server (machine) with limited capacity. Each job requests service in a prespecified time window and belon...

Berry's category of dI-domains with stable functions is a relatively intricate , yet elegant framework for semantics of programming languages. Despite over fteen years of work in the area, the exact reasons for dis-tributivity (Axiom d) and nitariness (Axiom I) have not been fully ex-plicated. This paper shows that Axiom d and Axiom I are important when one works within the realm of Scott-domai...

UNLABELLED Gene Ontology and other forms of gene-category analysis play a major role in the evaluation of high-throughput experiments in molecular biology. Single-category enrichment analysis procedures such as Fisher's exact test tend to flag large numbers of redundant categories as significant, which can complicate interpretation. We have recently developed an approach called model-based gene...

A process semantics for temporal logic specification is provided by relating a category of temporal theories and interpretations between theories where specification configuration and interconnection is achieved via colimits of diagrams, and a category of algebraic models of processes where parallel composition is explained in terms of limits of diagrams. This semantics is proved to be exact in...