Generalized Morita Theories The power of categorical algebra
نویسنده
چکیده
A solution to the problem posed by Isbell in the early 1970s of how to determine all varieties (in the sense of universal algebra) equivalent to a given variety is presented. The method is based on the use of Lawvere theories. It is shown how the known characterizations of rings, Morita equivalent to a given one, and of monoids, Morita equivalent to a given one, and also how (even an extension of) Hu’s primal algebra theorem become simple consequences hereof. Finally, a couple of related approaches is discussed. Mathematics Subject Classification (2000): Primary 16D90, 20M30, 03G05; Secondary 18C10.
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