A categorical approach to loops neardomains and nearfields
| Autor: | Rudger Kieboom, Tina Vervloet, Philippe Cara |
|---|---|
| Přispěvatelé: | Analytical, Categorical and Algebraic Topology, Mathematics-TW, Algebra |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
Pure mathematics
General Mathematics morphisms Mathematics - Category Theory 20N05 Group Theory (math.GR) 16A89 16A90 neardomains Morphism category Mathematics::Category Theory FOS: Mathematics Loops Point (geometry) Category Theory (math.CT) permutation set Mathematics - Group Theory Equivalence (measure theory) Categorical variable 12K05 20B22 Mathematics |
| Zdroj: | Vrije Universiteit Brussel Bull. Belg. Math. Soc. Simon Stevin 19, no. 5 (2012), 845-857 |
| Popis: | In this paper we study loops, neardomains and nearfields from a categorical point of view. By choosing the right kind of morphisms, we can show that the category of neardomains is equivalent to the category of sharply 2-transitive groups. The other categories are also shown to be equivalent with categories whose objects are sets of permutations with suitable extra properties. Up to now the equivalence between neardomains and sharply 2-transitive groups was only known when both categories were equipped with the obvious isomorphisms as morphisms. We thank Hubert Kiechle for this observation. Comment: to appear in Bull. Belg. Math. Soc. Simon Stevin |
| Databáze: | OpenAIRE |
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