# Homepage

I am a fourth year PhD candidate at the Mathematical Institute of Utrecht University where I work under the supervision of Lennart Meier.

## Research

My research interests lie in the realm of homotopy theory, particularly, I am interested in higher category theory and (equivariant) stable homotopy theory.

My PhD research is focused on the theory of double ∞-categories and a particular kind of these: so-called ∞-equipments. Every equipment has an associated formal category theory, and consequently, equipments are a good choice of ambient structures in which generalized ∞-categories live. A lot of category theory can be expressed using this technology! In particular, one may recover the foundations of internal, enriched, and fibered ∞-category theory via these equipments (and combined flavors!). The first part of this project has already appeared on the arXiv.

### Preprints and publications

Formal category theory in ∞-equipments I, submitted, arXiv:2308.03583, 56 pages.

A pasting theorem for iterated Segal spaces, Journal of Pure and Applied Algebra 228 (2024), no. 11, 107712, arXiv:2210.04549, 43 pages.

A short proof of the straightening theorem, with F. Hebestreit and G. Heuts, submitted, arXiv:2111.00069, 41 pages.

### In preparation

Formal category theory in ∞-equipments II.

The square-companion adjunction, with F. Abellán, V. Ozornova, and M. Rovelli.

### Theses

Grothendieck constructions in higher category theory, master's thesis, Utrecht University, August 2020.

## Contact

j (dot) c (dot) ruit (at) uu (dot) nl

Hans Freudenthalgebouw, room 5.03

Budapestlaan 6, 3584 CD Utrecht