Density presentations of functors

Abstract

The article contains the basic theory resulting from the presentation of a dense functor N: A → C by means of an expansion K(k, C) ० NJk ≅ C the term dense functor being used instead of the equivalent term left-adequate functor. Results by various authors on the density type of a functor are formulated in the V-context for V symmetric monoidal closed, and elementary proofs are given. In particular a characterisation theorem containing the well-known results of Beck and Ulmer is established.