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On locally small based algebraic theories. (English) Zbl 0598.18003

Author’s abstract: ”Locally small based algebraic theories are well-known to include varietal theories (in particular, classical algebraic theories) as well as most non-varietal theories of nature. Some examples are presented to show that some theorems for varietal theories are no more valid for locally small based theories. E.g., a locally small theory cannot be in general reconstructed from its category of algebras, and the category of algebras for a locally small based theory need not be canonically algebraic.”
Reviewer: E.Nelson

MSC:

18C10 Theories (e.g., algebraic theories), structure, and semantics
08C05 Categories of algebras
08B99 Varieties
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