Notions of generalized multicategory have been defined in numerous contexts throughout
the literature, and include such diverse examples as symmetric multicategories, globular …

In this thesis, we introduce Cartesian double categories, motivated by the work of Carboni,
Kelly, Walters, and Wood on Cartesian bicategories. Moving from bicategories to the slightly …

This book is an introduction to 2-categories and bicategories, assuming only the most
elementary aspects of category theory. A review of basic category theory is followed by a …

A multivariable adjunction is the generalisation of the notion of a 2-variable adjunction, the
classical example being the hom/tensor/cotensor trio of functors, to n+ 1 functors of n …

The purpose of this dissertation is to set up a theory of generalized operads and
multicategories, and to use it as a language in which to propose a definition of weak n …

We generalise the concepts introduced by Baez and Dolan to define opetopes constructed
from symmetric operads with a category, rather than a set, of objects. We describe the …

For a symmetric monoidal-closed category V and a suitable monad T on the category of sets,
we introduce the notion of reflexive and transitive (T, V)-algebra and show that various old …

A 2-CATEGORIES COMPANION 1. Overview and basic examples. This paper is a rather
informal guide to some of the basic theory of 2- Page 1 A 2-CATEGORIES COMPANION …

Category theory emerged in the 1940s in the work of Samuel Eilenberg and Saunders Mac
Lane. It describes relationships between mathematical structures. Outside of pure …

The basic concept in this paper is that of lax monoid in a monoidal bicategory. Interpreted in
the various duals of the monoidal bicategory of modules enriched over a good base …