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Extensivity of categories of relational structures

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Jason Parker

We prove that the category of models of any relational Horn theory satisfying a mild syntactic condition is infinitely extensive. Central examples of such categories include the categories of preordered sets and partially ordered sets, and the categories of small V-categories, (symmetric) pseudo-V-metric spaces, and (symmetric) V-metric spaces for a commutative unital quantale V. We also explicitly characterize initial sources and final sinks in such categories, and in particular embeddings and quotients.

Keywords:
relational Horn theory; extensive category; topological category; locally presentable category; concrete category; distributive category

2020 MSC:
06A06, 06F07, 18B50, 18C10, 18C35

*Theory and Applications of Categories,*
Vol. 38, 2022,
No. 23, pp 898-912.

Published 2022-07-07.

http://www.tac.mta.ca/tac/volumes/38/23/38-23.pdf

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