Homotopy Types of Abstract Elementary Classes
Tim Campion, Jinhe Ye

TL;DR
This paper demonstrates that for any given homotopy type, there exists an abstract elementary class whose classifying space has that homotopy type, illustrating a deep connection between homotopy theory and model theory.
Contribution
It constructs specific abstract elementary classes that realize any homotopy type as their classifying space, establishing a novel link between these mathematical areas.
Findings
Any homotopy type can be realized by an AEC's classifying space.
Constructs explicit examples of such AECs.
Shows the richness of AECs in modeling topological spaces.
Abstract
We prove that for any homotopy type , there is an abstract elementary class , with joint embedding, almagamation and no maximal models such that the classifying space realizes the homotopy type . We provide a few explicit examples.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
