Research Proposal: Towards a Non-Degenerate Cohesive Linear ∞-Topo
Year: 2026
Type: article
Abstract: This research proposal outlines a systematic programme to construct a non‑degenerate cohesive linear ∞‑topos, overcoming the degeneracy of the centre comonad model presented in [Woo 2026, DOI: 10.5281/zenodo.20412512]. After identifying the structural limitations of precomposition modalities and explaining why the derived centre (Hochschild cohomology) is unsuitable, the document explores four alternative directions: an abelianisation modality, a maximal commutative subalgebra site, the CPM construction, and a loop‑space approach via Hochschild homology. Each direction is analysed with precise mathematical hypotheses, open problems, and concrete first steps. A list of immediate mathematical tasks is provided. The proposal is intended as a research blueprint, inviting collaboration and further development.
Author: Woo, Joey
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7162811230
FWCI:
Cites:
Cited by:
Related to: