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Title: Day convolution for monoidal bicategories
Author: Corner, Alexander S.
ISNI:       0000 0004 6060 6872
Awarding Body: University of Sheffield
Current Institution: University of Sheffield
Date of Award: 2016
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Ends and coends can be described as objects which are universal amongst extranatural transformations. We describe a cate- gorification of this idea, extrapseudonatural transformations, in such a way that bicodescent objects are the objects which are universal amongst such transfor- mations. We recast familiar results about coends in this new setting, providing analogous results for bicodescent objects. In particular we prove a Fubini theorem for bicodescent objects. The free cocompletion of a category C is given by its category of presheaves [C^op ,Set]. If C is also monoidal then its category of presheaves can be pro- vided with a monoidal structure via the convolution product of Day. This monoidal structure describes [C^op ,Set] as the free monoidal cocompletion of C. Day’s more general statement, in the V-enriched setting, is that if C is a promonoidal V-category then [C^op ,V] possesses a monoidal structure via the convolution product. We define promonoidal bicategories and go on to show that if A is a promonoidal bicategory then the bicategory of pseudofunctors Bicat(A^op ,Cat) is a monoidal bicategory.
Supervisor: Gurski, Nick Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available