Analytic functors between presheaf categories over groupoids
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Peer-reviewed
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Abstract
The paper studies analytic functors between presheaf categories. Generalising results of A. Joyal and of R. Hasegawa for analytic endofunctors on the category of sets, we give two characterisations of analytic functors between presheaf categories over groupoids: (i) as functors preserving filtered colimits, quasi-pullbacks, and cofiltered limits; and (ii) as functors preserving filtered colimits and wide quasi-pullbacks. The development establishes that small groupoids, analytic functors between their presheaf categories, and quasi-cartesian natural transformations between them form a 2-category.
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Keywords
math.CT, math.CT
Journal Title
Theoretical Computer Science
Conference Name
Journal ISSN
0304-3975
Volume Title
546
Publisher
Elsevier BV