28 May 2018:
This week's progress:
1) Joe Moeller added a new idea to his paper on network models and submitted it for publication in Mathematical Structures in Computer Science
. He chose Pawel Sobocinski as the editor to submit to.
He also put the new version on the arXiv:
* Joe Moeller, Noncommutative network models
Abstract. Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by a monoid. A feature of the ordinary construction of network models is that it imposes commutativity relations between all edge components. Because of this, it cannot be used to model networks with bounded degree. In this paper, we construct the free network model on a given monoid, which can model networks with bounded degree. To do this, we generalize Green's graph products of groups to pointed categories which are finitely complete and cocomplete.
His new idea was that his construction of network models from monoids is really the left adjoint of the forgetful functor from network models to monoids! This makes it a lot more "conceptual".... and it should also be useful for designing networks.
2) Brandon Coya put his thesis on the arXiv:
* Brandon Coya, Circuits, Bond Graphs, and Signal-Flow Diagrams: A Categorical Perspective
3) In my online course I finished lecturing on Chapter 2 in Brendan and David's book. Check out some of these lectures:
* Resource theories
, 12 May 2018.
We came up with some interesting thoughts on economics and category theory, which I'll need to develop later.