variation models functors B op ×A → Set. By work of Street, both notions can be defined internally to an arbitrary 2-category or bicategory. While the twosided discrete fibrations model profunctors internally to Cat, unexpectedly, the dual two-sided codiscrete cofibrations are necessary to model V-profunctors internally to V-Cat. There are many categorical prerequisites, particularly in the later sections, but we believe they are strictly easier than the topics below that take advantage of them. These notes were written to accompany a talk given in the Algebraic Topology and Category Theory Proseminar in the fall of 2010 at the University of Chicago
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