Ideals, grills, primals and filters from the categorical viewpoint

Document Type : Original Paper

Authors

1 Department of Mathematics and Computer Sciences Sirjan University of Technology, Sirjan, Iran

2 faculty of payamenoor university

Abstract

In this paper, we study the categorical structures of the concepts of ideal, grill, primal, and filter, which play a fundamental and important role in the study of topology spaces. Some researchers have shown that all these concepts are equivalent, regardless of the categorical viewpoint. Here, we define the homomorphisms and so the category of each of these concepts and then show that all of them are isomorphic, except for the category of filters. As an important result, it has been shown that these categories are topological, except for the category of filters. Consequently, they are complete and cocomplete, but they are not algebraic. Thus, many topological properties can be easily expressed and analyzed in terms of each of these concepts. Finally, some categorical structures of ideals are described.

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History

  • Receive Date: 06 March 2024
  • Revise Date: 20 October 2024
  • Accept Date: 30 October 2024

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