摘要:

A quiver G (= directed multigraph, loops and parallel edges are allowed) is called a Hilbert basis quiver (HBQ) if a certain path algebra R[G] over a ring R is right noetherian provided R does. Such path algebras can be considered as generalized polynomial rings over R. There is the following characterization:

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632298

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The category of X-decomposable ordered vector spaces over a convenient category X is introduced and it is shown to uphold an exponential law [E8F,G] = [E,[F, G]] and to have limits and colimits. As the main special cases of X, the categories Cv (convergence spaces) and Bo (bornological spaces) are considered. The topological Cv-decomposable ordered vector spaces are precisely the ordered topological vector spaces whose positive cones give open decompositions.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632299

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

By defining a suitable adjoint process in the category of k-spaces, it is shown that systems that can be described by polynomial equations can be studied via the Arbib-Manes model of machines in a category. Basic results regarding reachability, observability and realization are derived from the general theory.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632300

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

A generalized rank condition is used to deduce necessary and sufficient conditions for the reachability and observability of a system in a category. A duality principle between reachability and observability is established. These results generalize those known previously for bilinear and linear systems over rings.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632301

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

Generalizing results of Herrlich and Nel, the author characterizes by means of smallest proper structures those objects X of an initially structured category for which X x—has a right adjoint, and describes the corresponding function spaces. It is shown that reduction to finally and initially dense classes is possible. The results are applied to epireflective subcategories of the category of limit spaces containing a finite non-indiscrete space, in particular to epireflective subcategories of TOP.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632302

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The fact that faithful functors are intimately connected with functors of topological type has been known for scene time. Here, we make the connection precise by introducing the notion of relatively topological functors, and characterize faithful functors as precisely those that are topological relative to a certain “natural” family of sources. Some other standard functor properties are also shown to have relative topological descriptions.

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632303

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632304

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

摘要:

The idea of adjoint functors or adjoint situation is one of the most important concepts in category theory. However, many examples are known which deviate from adjoint situations in one respect or another. These gave rise to various generalizations of adjoint situations (e.g. see R. Borger and w. Tholen [l], Y. Diers [2], and F. Ulmer [ll]).

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632305

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632306

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor

ISSN:1607-3606    

DOI:10.1080/16073606.1983.9632287

出版商:Taylor & Francis Group    

年代:1983

数据来源: Taylor