Online Archive of University of Virginia Scholarship
Segal Theta_2-monoids as monoidal (infty,1)-categories144 views
Author
Zapata Castro, Valentina, Mathematics - Graduate School of Arts and Sciences, University of Virginia
Advisors
Bergner, Julie
Abstract
In this thesis we establish a model structure for (infty, 2)-categories with a single object
based on Theta_2-spaces with prescribed Segal and completeness conditions. Then we build
a chain of Quillen equivalences between the previously mentioned model and a model
for monoidal (infty, 1)-categories, where we use the category of complete Segal spaces.
The comparison of models extends the categorical principle that monoids correspond
to categories with one object, adapting it to the realm of higher categories.
Zapata Castro, Valentina. Segal Theta_2-monoids as monoidal (infty,1)-categories. University of Virginia, Mathematics - Graduate School of Arts and Sciences, PHD (Doctor of Philosophy), 2025-08-02, https://doi.org/10.18130/nwmc-xk89.
