Year: 2026
Type: article
Abstract: We introduce the notion of virtual ultracategory. From a topological point of view, this notion can be seen as a categorification of relational β $\beta $ beta -modules. From a categorical point of view, virtual ultracategories generalize ultracategories in the same way that multicategories generalize monoidal categories. From a logical point of view, whereas the points of a coherent topos form an ultracategory, the points of an arbitrary topos form a virtual ultracategory. We then extend Makkai–Lurie’s conceptual completeness: a topos with enough points can be reconstructed from its virtual ultracategory of points.
Source: Journal of Symbolic Logic
Author: GABRIEL SAADIA
Institution: Stockholm University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W4416524137
FWCI:
Cites:
Cited by:
Related to: