Bicategories in Univalent Foundations

by   Benedikt Ahrens, et al.

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 those, we develop the notion of `displayed bicategories', an analog of displayed 1-categories introduced by Ahrens and Lumsdaine. Displayed bicategories allow us to construct univalent bicategories in a modular fashion. To demonstrate the applicability of this notion, we prove several bicategories are univalent. Among these are the bicategory of univalent categories with families and the bicategory of pseudofunctors between univalent bicategories. Our work is formalized in the UniMath library of univalent mathematics.


page 1

page 2

page 3

page 4


Univalent Monoidal Categories

Univalent categories constitute a well-behaved and useful notion of cate...

The Formal Theory of Monads, Univalently

We study the formal theory of monads, as developed by Street, in univale...

A Note on Generalized Algebraic Theories and Categories with Families

We give a new syntax independent definition of the notion of a generaliz...

Two-sided cartesian fibrations of synthetic (∞,1)-categories

Within the framework of Riehl-Shulman's synthetic (∞,1)-category theory,...

LNL polycategories and doctrines of linear logic

We define and study LNL polycategories, which abstract the judgmental st...

The Difference Lambda-Calculus: A Language for Difference Categories

Cartesian difference categories are a recent generalisation of Cartesian...

Substitution for Non-Wellfounded Syntax with Binders

We describe a generic construction of non-wellfounded syntax involving v...

Please sign up or login with your details

Forgot password? Click here to reset