Algebra and local presentability: how algebraic are they? (A survey)

J. Adámek, J. Rosický

This is a survey of results concerning the algebraic hulls of two 2-categories: VAR, the 2-category of finitary varieties, and LFP, the 2-category of locally finitely presentable categories. 

Tbilisi Mathematical Journal, Vol. 10(3) (2017), pp. 279-295