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

Reiterman, J.

Commentat. Math. Univ. Carol. 27, 325-340 (1986).

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

Keywords:

algebraic theories; varietal theories; locally small based theories