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An algebraic description of locally multipresentable categories

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Jiri Adamek, Jiri Rosicky

Locally finitely presentable categories are known to be
precisely the categories of models of essentially algebraic
theories, i.e., categories of partial algebras whose domains of
definition are determined by equations in total operations. Here
we show an analogous description of locally finitely
multipresentable categories. We also prove that locally
finitely multipresentable categories are precisely categories
of models of sketches with finite limit and countable coproduct
specifications, and we present an example of a locally
finitely multipresentable category not sketchable by a sketch
with finite limit and finite colimit specifications.

Keywords: locally multipresentable category, sketch.

AMS Classification (1991): 18C99.

*Theory and Applications of Categories*, Vol. 2, 1996, No. 4, pp 40-53.

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