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.