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 
@article{TAC_2022_38_a22,
     author = {Jason Parker},
     title = {Extensivity of categories of relational structures},
     journal = {Theory and applications of categories},
     pages = {898--912},
     publisher = {mathdoc},
     volume = {38},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a22/}
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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/