Duality in non-abelian algebra III. Normal categories and 0-regular varieties
| Autor: | Zurab Janelidze, Thomas Weighill |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Algebra and Number Theory
Functor 010102 general mathematics Duality (mathematics) Axiomatic system 0102 computer and information sciences 01 natural sciences Algebra Equivalence class (music) Congruence (geometry) 010201 computation theory & mathematics Mathematics::Category Theory 0101 mathematics Abelian group Categorical variable Axiom Mathematics |
| Zdroj: | Algebra universalis. 77:1-28 |
| ISSN: | 1420-8911 0002-5240 |
| DOI: | 10.1007/s00012-017-0422-7 |
| Popis: | Normal categories are pointed categorical counterparts of 0-regular varieties, i.e., varieties where each congruence is uniquely determined by the equivalence class of a fixed constant 0. In this paper, we give a new axiomatic approach to normal categories, which uses self-dual axioms on a functor defined using subobjects of objects in the category. We also show that a similar approach can be developed for 0-regular varieties, if we replace subobjects with subsets of algebras containing 0. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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