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Pseudo limits, biadjoints, and pseudo algebras: categorical foundations of conformal field theory
 Mem. Amer. Math. Soc
"... The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2category theory, such as versions of algebra, limit, colimit, and adjun ..."
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The purpose of this paper is to work out the categorical basis for the foundations of Conformal Field Theory. The definition of Conformal Field Theory was outlined in Segal [45] and recently given in [24] and [25]. Concepts of 2category theory, such as versions of algebra, limit, colimit, and adjunction, are necessary for this
TWOSIDED DISCRETE FIBRATIONS IN 2CATEGORIES AND BICATEGORIES
"... variation models functors B op ×A → Set. By work of Street, both notions can be defined internally to an arbitrary 2category or bicategory. While the twosided discrete fibrations model profunctors internally to Cat, unexpectedly, the dual twosided codiscrete cofibrations are necessary to model Vp ..."
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variation models functors B op ×A → Set. By work of Street, both notions can be defined internally to an arbitrary 2category or bicategory. While the twosided discrete fibrations model profunctors internally to Cat, unexpectedly, the dual twosided codiscrete cofibrations are necessary to model Vprofunctors internally to VCat. 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.