The importance of categorical reasoning in human cognition is well-established in psychology and cognitive science, and one of the most important functions of categorization is to facilitate prediction. This paper provides a model of optimal categorization. In the beginning of each period a subject observes a two-dimensional object in one dimension and wants to predict the object’s value in the...

‎This paper develops a basic theory of $H$-groups‎. ‎We‎ ‎introduce a special quotient of $H$-groups and‎ ‎extend some algebraic constructions of topological groups to the category‎ ‎of H-groups and H-maps and then present a functor from this category to the category of quasitopological groups‎.

in addition to exploring constructions and properties of limits and colimits in categories of topologicalalgebras, we study special subcategories of topological algebras and their properties. in particular, undercertain conditions, reflective subcategories when paired with topological structures give rise to reflectivesubcategories and epireflective subcategories give rise to epireflective subc...

these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

The present paper is devoted to the study of grill determinedL-approach merotopological spaces. The category having such spaces as objects is shown to be a topological construct (its initial and final structures are provided explicitly). The lattice structure of the family of all these spaces is also discussed. In the classical theory, this category (that is, when L = {0, 1}) is a supercategory...

Threshold agent networks (TANs) constitute a discretized modification of threshold (also known as neural) networks that are appropriate for modeling computer simulations. In this paper morphisms are introduced between TANs, thus forming a category TAN. Several of the properties of this category are explored. A generalization of TANs to allow more flexible interactions between the agents is then...

The goal of this survey paper is to argue that if orbifolds are groupoids, then the collection of orbifolds and their maps need to be thought of as a 2-category. This 2-category may be either taken to be the weak 2-category of groupoids, bibundles and equivariant maps between bibundles or the strict 2category of geometric stacks represented by proper etale Lie groupoids. While nothing in this p...

Deterministic recursive program schemes (RPS’s) have a clear category theoretic semantics presented by Ghani et al. and by Milius and Moss. Here we extend it to nondeterministic RPS’s. We provide a category theoretic notion of guardedness and of solutions. Our main result is a description of the canonical greatest solution for every guarded nondeterministic RPS, thereby giving a category theore...

We prove that the following two categories of sl(n,C)-modules are equivalent: 1) the category of modules with integral support filtered by submodules of Verma modules and complete with respect to Enright’s completion functor; 2) the category of all subquotients of modules F ⊗ M , where F is a finite-dimensional module and M is a fixed simple generic Gelfand-Zetlin module with integral central c...

The effect of typicality of category exemplars on naming performance was investigated using a single subject experimental design across participants and behaviors in four patients with fluent aphasia. Participants received a semantic feature treatment to improve naming of either typical or atypical examples, while generalization was tested on the untrained examples of the category. The order of...