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On essentially algebraic theories and their generalizations. (English) Zbl 0970.18006

The authors of the paper give a new proof of the fact that essentially algebraic theories form a syntax for locally presentable categories and describe an appropriate syntax for locally generated categories. Further they characterize locally multirepresentable categories and provide an analogous syntax also for this case. Some of the presented proofs simplify those from the book of J. Adámek and J. Rosický [“Locally presentable and accessible categories”, Cambridge Univ. Press, Cambridge (1994; Zbl 0795.18007)].

MSC:

18C10 Theories (e.g., algebraic theories), structure, and semantics
08A55 Partial algebras
18C35 Accessible and locally presentable categories

Citations:

Zbl 0795.18007
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