Every 2-Segal space is unital (with Richard Garner, Joachim Kock, May U. Proulx, and Mark Weber). Communications in Contemporary Mathematics 23 (2021), 2050055 arXiv:1905.09580


Generalizing quasi-categories via model structures on simplicial sets. arXiv:2111.06512

A horn-like characterization of the fibrant objects in the minimal model structure on simplicial sets. (In preparation.)

Quasi-2-Segal sets. (In preparation.)

Current Projects:

  • Constructing a Cisinski model structures for an "infinity" version of 2-Segal sets. Also, providing a description of the fibrant objects in the minimal Cisinski model structure in terms of a new kind of horn extension.

  • Identifying a simple criterion for when weakly k-excisive simplicial objects (which Walde showed are precisely those which satisfy a higher Segal condition) are k-excisive in the more familiar sense from Goodwillie calculus.