We characterize the equational theories and Lawvere theories that correspond to the categories of analytic and polynomial monads on Set, and hence also the categories of the symmetric and rigid operads in Set. We show that the category of analytic monads is equivalent to the category of regular-linear theories. The category of polynomial monads is equivalent to the category of rigid theories, i...

The notion of central series for groups with action on itself is introduced. An analogue of Witt’s construction is given for such groups. A certain condition is found for the action and the corresponding category is defined. It is proved that the above construction defines a functor from this category to the category of Lie–Leibniz algebras and in particular to Leibniz algebras; also the restri...

I introduce the notion of probability sheaf, which is a mathematical structure capturing the relationship between probabilistic concepts (such as random variable) and sample spaces. Various probability-theoretic notions can be (re)formulated in terms of category-theoretic structure on the category of probability sheaves. As a main example, I consider the Giry monad, which, in its original formu...

The notion of proof-net category defined in this paper is closely related to graphs implicit in proof nets for the multiplicative fragment without constant propositions of linear logic. Analogous graphs occur in Kelly’s and Mac Lane’s coherence theorem for symmetric monoidal closed categories. A coherence theorem with respect to these graphs is proved for proof-net categories. Such a coherence ...

Simple and semisimple additive categories are studied. We prove, for example, that an artinian additive category is (semi)simple iff it is Morita equivalent to a division ring(oid). Semiprimitive additive categories (that is, those with zero radical) are those which admit a noether full, faithful functor into a category of modules over a division ringoid. Mathematics Subject Classifications (19...

We give a constructive characterization of morphisms between open sublocales of localic completions of locally compact metric (LCM) spaces, in terms of continuous functions. The category of open subspaces of LCM spaces is thereby shown to embed fully faithfully into the category of locales (or formal topologies). 2000 Mathematics Subject Classification 03F60, 18B30, 54E99 (primary)

Let M be a non–compact, connected manifold of dimension ≥ 1. Let D(sheaves/M) be the unbounded derived category of chain complexes of sheaves of abelian groups on M . We prove that D(sheaves/M) is not a compactly generated triangulated category, but is well generated. 2000 Mathematics Subject Classification: 18E30 55P99 55U35

This paper proposes a generation method of a subject-specific Facial Expression Map (FEMap) using the Self-Organizing Maps (SOM) of unsupervised learning and Counter Propagation Networks (CPN) of supervised learning together. The proposed method consists of two steps. In the first step, the topological change of a face pattern in the expressional process of facial expression is learned hierarch...

Let S-Top be the category of topological S-acts over a topological semigroup S and S-SemiTop be the category of semitopological S-acts over a semitopological semigroup S. It is obvious that any topological S-act is a semitopological S-act, however we will see that the converse is not true in general. In this note, we study the universal objects in the category of semitopological S-acts and intr...