Announcement: second CATNIP meeting, University of Strathclyde, Glasgow
Jules Hedges
The second Categories Network Project (CATNIP) meeting will be held at Strathclyde on Monday 4th December
The talks will be in the McCance building in room MC301. Arrival and coffee will be at 10.30, the first talk at 11.00, and the last talk will finish at 17.00
Speakers & abstracts:
Rita (Fatimah) Ahmadi - Bicategory of Topological Quantum Computation
Unitary Ribbon Fusion Categories (URFC) formalise anyonic theories. It has been widely assumed the same category formalises a model of topological quantum computation. However, we recently addressed and resolved this confusion and demonstrated while the former could be any fusion category, the latter is always a subcategory of \textbf{Hilb}. In this talk, I argue a categorical formalism which captures and unifies both an anyonic theory and corresponding models of topological quantum computation is a braided (fusion) bicategory.
John Baez - Software for Compositional Modeling
Mathematical models of human interactions are important and widely used in epidemiology, but building and working with these models at scale is challenging. I will explain two software tools for doing this, both based on category theory. Modelers often regard diagrams as an informal step toward a mathematically rigorous formulation of a model. Giving these diagrams a precise syntax using category theory has many advantages, but I will focus on those connected to "community based modeling": the process of working with diverse community members to build a model. The next step is to tackle "agent-based models" and use them to help plan our response to climate change.
Neil Ghani - TBA
Dan Marsden - The Graphical Theory of Monads
The formal theory of monads shows that much of the theory of monads
can be developed in the abstract at the level of 2-categories. This
means that results about monads can established once and for all, and
simply instantiated in settings such as enriched category theory.
Unfortunately, these results can be hard to reason about as they
involve more abstract machinery. In this talk, I shall present the formal
theory of monads in terms of string diagrams --- a graphical language
for categorical calculations. Using this perspective, I will show that
many aspects of the theory of monads, such as the Eilenberg-Moore and
Kleisli resolutions of monads, liftings, and distributive laws can be
understood in terms of systematic graphical calculational reasoning.
The talk will serve as an introduction both to the formal theory of
monads and to the use of string diagrams in non-trivial calculations,
in particular, their application to calculations in monad theory.
(Joint work with Ralf Hinze)