One goal of applied category theory is to understand open systems in a
compositional manner. We compare two ways of describing open systems
as cospans equipped with extra data — structured and decorated
cospans — and explain a generalization of Fong's original
decorated cospans which allows the extra data to be an object in a
category, rather than merely an element of a set. We state a
sufficient condition for decorated cospans to be equivalent to
structured cospans, and end with a number of open questions. This is
joint work with Kenny Courser and Christina Vasilakopoulou.
You can see the slides of this talk here. Click on items
in red for more details! Here's a video
of the talk:
Stock-flow diagrams are widely used in epidemiology to model the
dynamics of populations. Although tools already exist for building
these diagrams and simulating the systems they describe, we have
created a new package called StockFlow, part of the AlgebraicJulia
ecosystem, which uses ideas from category theory to overcome notable
limitations of existing software. Compositionality is provided by the
theory of decorated cospans: stock-flow diagrams can be composed to
form larger ones in an intuitive way formalized by the operad of
undirected wiring diagrams. Our approach also cleanly separates the
syntax of stock and flow diagrams from the semantics they can be
assigned. We consider semantics in ordinary differential equations,
although others are possible. As an example, we explain code in
StockFlow that implements a simplified version of a COVID-19 model
used in Canada. This is joint work with Xiaoyan Li, Sophie Libkind,
Nathaniel Osgood and Evan Patterson.
You can see the slides of this talk
here. Click on items in blue for more details!
Here's a video of the talk:
