Adámek, Jiří; Hébert, M.; Rosický, Jiří On essentially algebraic theories and their generalizations. (English) Zbl 0970.18006 Algebra Univers. 41, No. 3, 213-227 (1999). 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)]. Reviewer: Jiří Rachůnek (Olomouc) Cited in 3 Documents MSC: 18C10 Theories (e.g., algebraic theories), structure, and semantics 08A55 Partial algebras 18C35 Accessible and locally presentable categories Keywords:essentially algebraic theory; locally presentable category; locally multigenerated category Citations:Zbl 0795.18007 PDFBibTeX XMLCite \textit{J. Adámek} et al., Algebra Univers. 41, No. 3, 213--227 (1999; Zbl 0970.18006) Full Text: DOI