Topic
Connected category
About: Connected category is a research topic. Over the lifetime, 6 publications have been published within this topic receiving 18 citations.
Papers
Patent•
13 Nov 2013
TL;DR: In this article, a system having a processor is programmed to realize practical quantitative assessment of similarity of categorized data, which may be stored in a memory as a category graph comprising a graphical data structure having plural parent and child category nodes connected by directed edges, such that sequences of connected category nodes represent hierarchical relations between categories of objects.
Abstract: A system having a processor is programmed to realize practical quantitative assessment of similarity of categorized data. The category data may be stored in a memory as a category graph comprising a graphical data structure having plural parent and child category nodes connected by directed edges, such that sequences of connected category nodes represent hierarchical relations between categories of objects. A similarity metric of a selected pair of categories may be derived, in one embodiment, by analysis of ancestors of the selected pair of categories, including consideration of closest common ancestors in the category graph. Efficiency improvements may include transforming a directed cyclic graph to a directed acyclic graph, and optionally deriving a subgraph to reduce the number of categories under consideration. The software methods may further comprise computing a similarity metric for a pair of objects based on the similarity score for the corresponding pair of categories.
9 citations
Posted Content•
TL;DR: In this paper, the theory of coverings of a small connected category B was developed and it was shown that the category of Galois coverings for B is equivalent to the category for Galois covers of its fundamental groupoid.
Abstract: In this paper we develop the theory of coverings of a small connected category B. We show that the category of Galois coverings of B is equivalent to the category of Galois coverings of its fundamental groupoid. Making use of effective gradings of B we explicitly construct Galois coverings through a smash product analogous to the one considered in the linear case, see [4, 7]. In particular, the universal cover of B can be obtained from its fundamental groupoid. 2010 MSC: 20L05, 18A32, 18A22
8 citations
TL;DR: In this article, the tensor product of Q-P quantale modules is obtained, and some properties of their properties are discussed, and the structure of the limit of this category is given.
Abstract: In this paper, firstly, the definition of Q-P quantale modules and some relative concepts were introduced. we prove that the category of Q-P quantale modules is a pointed and connected category. Secondly, we give the structure of the limit of this category, so it is complete. At last, The definition of bimorphism of Q-P quantale modules is given. The tensor product of Q-P quantale modules is obtained, and some of their properties are discussed.
1 citations
1 Jan 2010
1 citations
1 Jan 2006
TL;DR: In this article, the existence of non-complemented and recursively inseparable domains in a locally connected category is shown to be local connected if connected domains are jointly epimorphic, and the results are generalized to non-local connected categories by transporting the range restriction category structure of a non-locally connected recursion category to a local connected restriction category by means of a range functor.
Abstract: A recursion category is locally connected if connected domains are jointly epimorphic. New proofs of the existence of non-complemented and recursively inseparable domains are given in a locally connected category. The use of local connectedness to produce categorical analogs of undecidable problems is new; the approach allows us to relax the hypotheses under which the results were originally proved. The results are generalized to non-locally connected recursion categories by transporting the range restriction category structure of a non-locally connected recursion category to a locally connected restriction category by means of a range functor; i.e., a functor that preserves coproducts, restrictions and ranges; a range functor need not preserve the near-product.
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 1 |
| 2016 | 1 |
| 2013 | 1 |
| 2012 | 1 |
| 2010 | 1 |
| 2006 | 1 |