Fraïssé Limits in Comma Categories
| Autor: | Maja Pech, Christian Pech |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Model theory
Monoid Pure mathematics Algebra and Number Theory Endomorphism General Computer Science Comma category 010102 general mathematics Structure (category theory) 0102 computer and information sciences Droste effect 01 natural sciences Theoretical Computer Science 010201 computation theory & mathematics Mathematics::Category Theory Theory of computation 0101 mathematics Categorical variable Mathematics |
| Zdroj: | Applied Categorical Structures. 26:799-820 |
| ISSN: | 1572-9095 0927-2852 |
| DOI: | 10.1007/s10485-018-9519-1 |
| Popis: | Fraisse’s theorem characterizing the existence of universal homogeneous structures is a cornerstone of model theory. A categorical version of these results was developed by Droste and Gobel. Such an abstract version of Fraisse theory allows to construct unusual objects that are far away from the usual structures. In this paper we are going to derive sufficient conditions for a comma category to contain universal homogeneous objects. Using this criterion, we characterize homogeneous structures that possess universal homogeneous endomorphisms. The existence of such endomorphisms helps to reduce questions about the full endomorphism monoid to the self-embedding monoid of the structure. As another application we characterize the retracts of homogeneous structures that are induced by universal homogeneous retractions. This extends previous results by Bonato, Delic, Mudrinski, Dolinka, and Kubiś. |
| Databáze: | OpenAIRE |
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