A locally strongly finitely presentable category is like a locally finitely presentable category, but where the class of filtered colimits (respectively the class of finite limits) is replaced by the class of sifted colimits (respectively the class of finite products).
Locally strongly finitely presentable category are precisely those categories equivalent to varieties of algebras.
Jiri Adamek, Jiri Rosicky, On sifted colimits and generalized varieties, TAC 8 (2001) pp.33-53. (tac)
Jiri Adamek, Jiri Rosicky, Enrico Vitale, What are sifted colimits?, TAC 23 (2010) pp. 251–260. (tac)
Jiri Adamek, Jiri Rosicky, Enrico Vitale, Algebraic Theories - a Categorical Introduction to General Algebra , Cambrige UP 2010. (ch. 2) (draft)
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