Towards higher topology

0544168 - MÚ 2023 RIV NL eng J - Journal Article
Di Liberti, Ivan
Towards higher topology.
Journal of Pure and Applied Algebra. Roč. 226, č. 3 (2022), č. článku 106838. ISSN 0022-4049. E-ISSN 1873-1376
R&D Projects: GA ČR(CZ) GX20-31529X
Institutional support: RVO:67985840
Keywords : topological space * higher topology * Scott adjunction
OECD category: Pure mathematics
Impact factor: 0.8, year: 2022
Method of publishing: Limited access
https://doi.org/10.1016/j.jpaa.2021.106838

We categorify the adjunction between locales and topological spaces, this amounts to an adjunction between (generalized) bounded ionads and topoi. We show that the adjunction is idempotent. We relate this adjunction to the Scott adjunction, which was discussed from a more categorical point of view in [21]. We hint that 0-dimensional adjunction inhabits the categorified one.
Permanent Link: http://hdl.handle.net/11104/0321218