You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Jean-Baptiste Vienney (Aug 07 2023 at 04:07):Hi, I put this preprint on the ArXiv:
https://arxiv.org/abs/2308.02094
Title: String diagrams for symmetric powers I: In symmetric monoidal Q≥0-linear categories
Abstract: Symmetric powers are an important notion in mathematics, computer science and physics. In mathe- matics, they are used to build symmetric algebras, in computer science, to build free exponential modal- ities of linear logic and in physics, Fock spaces. We study symmetric powers through the lens of category theory. We focus here on the simpler case where nonnegative rational scalars are available ie. we study symmetric powers in symmetric monoidal Q≥0-linear categories. Among the developments, a main point is the introduction of the notion of binomial graded bimonoid and the associated string diagrams which characterize symmetric powers in this setting.
I would gladly receive any comment about it! I'm happy because this is the first paper I write alone (and my second one in total) but I'm also a bit more uncertain about it because of this same fact :smile: