Geodesic
Extensivity of categories of relational structures
Theory and applications of categories, Tome 38 (2022), pp. 898-912

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Publié le :
Classification : 06A06, 06F07, 18B50, 18C10, 18C35
Keywords: relational Horn theory, extensive category, topological category, locally presentable category, concrete category, distributive category 
Jason Parker. Extensivity of categories of relational structures. Theory and applications of categories, Tome 38 (2022), pp. 898-912. http://geodesic.mathdoc.fr/item/TAC_2022_38_a22/
@article{TAC_2022_38_a22,
     author = {Jason Parker},
     title = {Extensivity of categories of relational structures},
     journal = {Theory and applications of categories},
     pages = {898--912},
     year = {2022},
     volume = {38},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a22/}
}
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