Semicategories and Sheaf Theory

Authors

Dale Garraway, Eastern Washington University

Document Type

Presentation Abstract

Presentation Date

3-22-2011

Abstract

A sheaf on a Heyting algebra H is a functor F : H^op → SET that satisfies the Gluing axiom. In this talk we explore sheaves from a semicategorical perspective and show that a sheaf is an idempotent semifunctor F : H^co → REL. The key difference in the outlook is that in the usual sheaf theoretical perspective H is interpreted as a multi object category while the semicategory setting views H as an one object supremum enriched semicategory. Using this latter perspective we expand on Higg's Q-valued set version of sheaf theory to construct a semicategory theory of sheaves in terms of semifunctors.

Additional Details

Tuesday, 22 March 2011
1:10 p.m. in Math 211
4:00 p.m. Refreshments in Math Lounge 109

Recommended Citation

Garraway, Dale, "Semicategories and Sheaf Theory" (2011). Colloquia of the Department of Mathematical Sciences. 369.
https://scholarworks.umt.edu/mathcolloquia/369