Dyckerhoff–Kapranov–Schechtman–Soibelman simplex 2-category conjecture
The simplex -category construction is conjectured to satisfy the model-independent universal characterization proposed by Dyckerhoff–Kapranov–Schechtman–Soibelman. The supplied sources do not state the universal property explicitly enough to give its full quantifiers and hypotheses.
References
Primary source
Additional references
- Free bifibrations of (∞,2)-categories, 2-simplicial objects and the walking adjunction — arXiv — Fernando Abellán
Progress summary
An unrefereed preprint claims to prove the conjecture, but the result has not been independently verified.
The conjecture asserts a model-independent universal characterization for a simplex -category construction in higher category theory. No proposer or original date is identified in the retrieved sources.
September 2026 claimed proof
Fernando Abellán claims that a fibrational construction for freely adjoining adjoints establishes the conjectured universal characterization, together with a new proof of the walking adjunction theorem. The preprint presents this as a resolution, but no independent verification, referee report, counterexample, or competing proof was found.
Current status (as of September 2026): A preprint claims the conjecture is solved, but the claim remains unverified.
Solutions 0
No solutions have been posted yet.