Category theory is a branch of mathematics that provides a formal framework for
understanding the relationship between mathematical structures. To this end, a category not …

Enriched categories are categories whose sets of morphisms are enriched with extra
structure. Such categories play a prominent role in the study of higher categories, homotopy …

In previous work (" From signatures to monads in UniMath"), we described a category-
theoretic construction of abstract syntax from a signature, mechanized in the UniMath library …

Univalent categories constitute a well-behaved and useful notion of category in univalent
foundations. The notion of univalence has subsequently been generalized to bicategories …

Abstract The Univalence Principle is the statement that equivalent mathematical structures
are indistinguishable. We prove a general version of this principle that applies to all set …

We present a formalization of different categorical structures used to interpret linear logic.
Our formalization takes place in UniMath, a library of univalent mathematics based on the …

Polynomial functors are a categorical generalization of the usual notion of polynomial, which
has found many applications in higher categories and type theory: those are generated by …

We propose a general notion of model for two-dimensional type theory, in the form of
comprehension bicategories. Examples of comprehension bicategories are plentiful; they …

In this paper, we study finitary 1-truncated higher inductive types (HITs) in homotopy type
theory. We start by showing that all these types can be constructed from the groupoid …

We develop the formal theory of monads, as established by Street, in univalent foundations.
This allows us to formally reason about various kinds of monads on the right level of …