12 citations · 31 across the 7 of their papers we have counts for
9 papers
Composing Double Categories
Mitchell Buckley, Richard Garner
Many kinds of generalised syntax, including internal categories, T-categories or polynomial monads, arise as monads in bicategories of a certain flavour: maps are some kind of span…
A Larson-Sweedler Theorem for Hopf V-Categories
Mitchell Buckley, Timmy Fieremans, Christina Vasilakopoulou +1
The aim of this paper is to extend the classical Larson-Sweedler theorem, namely that a k-bialgebra has a non-singular integral (and in particular is Frobenius) if and only if it i…
Oplax Hopf Algebras
Mitchell Buckley, Timmy Fieremans, Christina Vasilakopoulou +1
We introduce the notion of an oplax Hopf monoid in any braided monoidal bicategory, generalizing that of a Hopf monoid in a braided monoidal category in an appropriate way. We show…
Orientals and cubes, inductively
Mitchell Buckley, Richard Garner
We provide direct inductive constructions of the orientals and the cubes, exhibiting them as the iterated cones, respectively, the iterated cylinders, of the terminal strict globul…
Formalizing parity complexes
Mitchell Buckley
We formalise, in Coq, the opening sections of Parity Complexes [Street1991] up to and including the all important excision of extremals algorithm. Parity complexes describe the ess…
The Catalan simplicial set II
Mitchell Buckley
The Catalan simplicial set is known to classify skew-monoidal categories in the sense that a map from to a suitably defined nerve of is pre…
The Catalan simplicial set
Mitchell Buckley, Richard Garner, Stephen Lack +1
The Catalan numbers are well-known to be the answer to many different counting problems, and so there are many different families of sets whose cardinalities are the Catalan number…
Skew-monoidal categories and the Catalan simplicial set
Mitchell Buckley, Richard Garner, Stephen Lack +1
The basic data for a skew-monoidal category are the same as for a monoidal category, except that the constraint morphisms are no longer required to be invertible. The constraints a…
Fibred 2-categories and bicategories
Mitchell Buckley
We generalise the usual notion of fibred category; first to fibred 2-categories and then to fibred bicategories. Fibred 2-categories correspond to 2-functors from a 2-category into…