Categorical Spectra with Adjoints

May 21, 2026 PIRSA:26050062 Scientific Series Mathematical physics

Masuda, N. (2026). Categorical Spectra with Adjoints. Perimeter Institute. https://pirsa.org/26050062

Masuda, Naruki. Categorical Spectra with Adjoints. Perimeter Institute, May. 21, 2026, https://pirsa.org/26050062

@misc{ pirsa_PIRSA:26050062,
  doi = {10.48660/26050062},
  url = {https://pirsa.org/26050062},
  author = {Masuda, Naruki},
  keywords = {Mathematical physics},
  language = {en},
  title = {Categorical Spectra with Adjoints},
  publisher = {Perimeter Institute},
  year = {2026},
  month = {may},
  note = {PIRSA:26050062 see, \url{https://pirsa.org}}
}

Abstract

Categorical spectra generalize spectra by allowing each level to be a pointed (∞,∞)-category rather than a space(=(∞,0)-category). After reviewing facts on Gray tensor products and stability of Gray-enriched categories, we will focus on what happens when we ask each level to have adjoints. We will in particular make some observations based on/related to the cobordism hypotheses.