The term “logos” is used
by Heraclitus for logos (in philosophy), something that later was discussed as “logic” in Hegel‘s Science of Logic.
in Freyd-Scedrov as a synonym for Heyting category;
in Joyal 08 as a synonym for quasi-category ((∞,1)-category, cf. also Joyal locus);
in Joyal 2015, Anel & Joyal 2019, ABFJ 2023 p. 3 for the formal dual of a topos, namely for an object of the opposite of the category of toposes. This is along the same lines as the classical formal duality between frames and locales ((0,1)-toposes) and extends immediately to $(\infty,1)$-toposes whose formal duals are hence “$(\infty,1)$-logoi” or “$\infty$-logoi”, for short;
in Anel 2019 for a cartesian closed $\infty$-category with finite $\infty$-limits and van Kampen colimits in size bounded by some inaccessible cardinal.
in DLL24 for a cocomplete category equipped with a family of limits such that colimits are exact with respect to this family. This paper also discusses the relationship between theirs, Anel-Joyal and Freyd-Scedrov proposal of logos. Despite being different these proposals all come with similar motivations in mind.
Peter Freyd, Andre Scedrov, Categories, Allegories
André Joyal, Notes on Logoi, 2008 (pdf)
André Joyal, A crash course in topos theory : the big picture, lecture series at Topos à l’IHÉS, 2015 Video 1, Video 2, Video 3, Video 4.
Mathieu Anel, André Joyal, Topo-logie, in New Spaces for Mathematics and Physics, Cambridge University Press (2021) 155-257 [doi:10.1017/9781108854429.007, pdf]
Mathieu Anel, Descent and Univalence, talk at HoTTEST (May 2019) [slides, video]
Mathieu Anel, Georg Biedermann, Eric Finster, André Joyal, Left-exact Localizations of ∞-Topoi III: The Acyclic Product [arXiv:2308.15573]
Ivan Di Liberti, Gabriele Lobbia, Sketches and Classifying Logoi [arXiv:2403.09264]
Discussion of relation to taoism?:
Last revised on March 25, 2024 at 19:41:00. See the history of this page for a list of all contributions to it.