Bicategories in univalent foundations
Year: 2021
Type: article
Abstract: We develop bicategory theory in univalent foundations. Guided by the notion of univalence for (1-)categories studied by Ahrens, Kapulkin, and Shulman, we define and study univalent bicategories. To construct examples of univalent bicategories in a modular fashion, we develop displayed bicategories, an analog of displayed 1-categories introduced by Ahrens and Lumsdaine. We demonstrate the applicability of this notion and prove that several bicategories of interest are univalent. Among these are the bicategory of univalent categories with families and the bicategory of pseudofunctors between univalent bicategories. Furthermore, we show that every bicategory with univalent hom-categories is weakly equivalent to a univalent bicategory. All of our work is formalized in Coq as part of the UniMath library of univalent mathematics.
Institutions: Radboud University Nijmegen, University of Florence
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,255
Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Ministero dell’Istruzione, dell’Università e della Ricerca, Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni, Engineering and Physical Sciences Research Council, Air Force Office of Scientific Research
OpenAlex ID: W2955888331