Geodesic
The matrix taxonomy of finitely complete categories
Theory and applications of categories, Tome 38 (2022), pp. 737-790

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

This paper is concerned with the taxonomy of finitely complete categories, based on 'matrix properties' - these are a particular type of exactness properties that can be represented by integer matrices. In particular, the main result of the paper gives an algorithm for deciding whether a conjunction of such properties implies another such property. Computer implementation of this algorithm allows one to peer into the complex structure of the poset of `matrix classes', i.e., the poset of all collections of finitely complete categories determined by matrix properties. Among elements of this poset are the collections of Mal'tsev categories, majority categories, (finitely complete) arithmetical categories, as well as finitely complete extensions of various classes of varieties defined by a special type of Mal'tsev conditions found in the literature.

Publié le :
Classification : 03B35, 18E13, 18-08, 08B05, 68V20, 03G30 (primary), 68V05, 18A35, 18B15, 03C35, 08C05 (secondary)
Keywords: finitely complete category, poset of matrix properties, computer-generated proof, Mal'tsev category, majority category, arithmetical category 
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     author = {Michael Hoefnagel and Pierre-Alain Jacqmin and Zurab Janelidze},
     title = {The matrix taxonomy of finitely complete categories},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a18/}
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Michael Hoefnagel; Pierre-Alain Jacqmin; Zurab Janelidze. The matrix taxonomy of finitely complete categories. Theory and applications of categories, Tome 38 (2022), pp. 737-790. http://geodesic.mathdoc.fr/item/TAC_2022_38_a18/