Analytic functors between presheaf categories over groupoids

作者：Fiore Marcelo^*

来源：Theoretical Computer Science, 2014, 546: 120-131.

DOI：10.1016/j.tcs.2014.03.004

• Free symmetric monoidal category
• Analytic functor
• Presheaf category
• Groupoid

The paper studies analytic functors between presheaf categories. Generalising results of A. loyal [11] and R. Hasegawa [9] 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.

• 出版日期2014-8-21