Abstract
Characterizations of set-valued weakly flat (in B. Stenström's sense) functors over small categories C , describing the structure of those functors from different points of view (categorical and universal algebraic), have been obtained. This result not only generalizes, but also combines and supplements, all related results so far known for S-acts. The approach taken is based on exploiting diagrams of functors similar to one used by Mac Lane and Moerdijk for describing flat functors.
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