Dense Functors

Giacomo Tendas

A (fully faithful) functor J:A->B is called “dense" if every object of B is canonically a colimit of objects taken from its subcategory A. These functors arise everywhere in category theory, e.g: in the setting of free cocompletions of categories under certain colimits, in free exact completions of lex categories, in the proof of Barr’s embedding for regular categories, and in the category of algebras for a monad. The aim of this talk is to see various equivalent definitions of density and to understand why they are useful in the constructions mentioned above.

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