Geodesic
A characterization of the category of a quasiprimitive class of universal algebras and its correspondences
Sbornik. Mathematics, Tome 11 (1970) no. 1, pp. 65-74 
G. E. Rivlin. A characterization of the category of a quasiprimitive class of universal algebras and its correspondences. Sbornik. Mathematics, Tome 11 (1970) no. 1, pp. 65-74. http://geodesic.mathdoc.fr/item/SM_1970_11_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

If $\Omega$ is the class of all universal algebras with the system of operations $\Omega$, then all homomorphisms of $\Omega$-algebras form a category. In this article we find necessary and sufficient conditions under which an arbitrary category is isomorphic to a full subcategory of the category of $\Omega$-algebras closed with respect to direct products and subalgebras. We also find necessary and sufficient conditions under which a given category with involution is isomorphic to some full subcategory of the category of correspondences of $\Omega$-algebras. Bibliography: 8 titles.

[1] J. R. Isbell, “Adequate subcategories”, Illinois J. Math., 4:4 (1960), 541–552 | MR | Zbl

[2] D. Puppe, “Korrespondenzen über abelschen Kategorien”, Math. Ann., 148 (1962), 1–30 | DOI | MR | Zbl

[3] A. I. Maltsev, “Kvaziprimitivnye klassy abstraktnykh algebr”, DAN SSSR, 108:2 (1956), 187–189

[4] A. G. Kurosh, A. X. Livshits, E. G. Shulgeifer, “Osnovy teorii kategorii”, Uspekhi matem. nauk, XV:6(96) (1960), 3–52 | MR

[5] J. R. Isbell, “Subobject, adequacy, completeness and categories of algebras”, Rozprawy Mat., 36 (1964), 1–32 | MR

[6] F. W. Lawvere, Fuctional semantics of algebraic theories, Thesis, Columbia, 1963 | Zbl

[7] F. E. J. Linton, “Some aspects of equational categories”, Proc. of the Conference on Categorial Algebra (La Jolla 1965), Berlin–Heidelberg, 1966, 84–94 | MR | Zbl

[8] W. Felscher, “Kennzeichnung von primitiven und quasiorimitiven Kategorien von Algebren”, Arch. Math., XIX (1968), 390–397 | DOI | MR