#appliedcategorytheory — Public Fediverse posts

I am always careful, when discussing the organization of organisms, because saying things like "the whole is not the sum of its parts" makes people think I'm talking about vitalism or religion or something, but I'm talking about non-cartesian products which lack projections #RM3 #SMCC #AppliedCategoryTheory

I am always careful, when discussing the organization of organisms, because saying things like "the whole is not the sum of its parts" makes people think I'm talking about vitalism or religion or something, but I'm talking about non-cartesian products which lack projections #RM3 #SMCC #AppliedCategoryTheory

This year's Joint Mathematics Meetings in San Francisco is going to be pretty chill for me. This is my fourth #JMM and my third in person. Last year I organized a session on #AppliedCategoryTheory, but this time around I'm just giving a couple talks on #MachineLearning and the history of the #Bourbaki group.

#JMM2024

I'm giving another talk on discrete neural nets and polymorphic learning at the #CUBoulder PALS seminar (https://math.colorado.edu/algebralogic) at 230pm MDT today! You can find the preprint I'm discussing at https://arxiv.org/abs/2308.00677. As usual, a recording will be available in case you'd like to watch later.

#AI #CategoryTheory #algebra #AbstractAlgebra #Combinatorics #ComputerScience #AppliedCategoryTheory

"This talk is an invitation to embark on a journey to solve one of the most naive yet insanely convoluted open question in #software architecture: the problem of unit systems and physical quantities. As surprising as it may seem, in 2023, there is still no software library available in any of the most common programming languages that covers the issue in its full complexity including its myriad of edge cases. In the context of a standardization effort within the #cpp programming language committee #WG21 on the topic of units this talk constitutes an attempt to reach out to the #appliedcategorytheory community in order to approach the subject from a new angle.

Throughout the presentation, a particular attention will be put on the underlying reasons behind the emerging complexity of the subject and why applied category theory may be key to disentangle this apparent complexity. This will be illustrated by concrete applications in computational #physics and metrology, including particularly pathological cases that will put into question the very notion of what a unit is. Exploring conceptual boundaries through edge cases will help putting constraints on the mathematical structures that may be used to abstract the problem. Beyond the mere scope of being able to standardize a unit systems software library, the challenge raised in this talk represents a gateway to deep questions about physics, its language, its structure, and how to translate it into #typetheory. It also constitutes a perfect playground for applied category theory, going from a naive and well-framed question to an interdisciplinary open problem at the intersection of physics, computer science, and mathematics with broad impacts for programming languages and international standards."

https://www.youtube.com/watch?v=6Fc-mjFMSrw

@abuseofnotation There are at least two reasons that categories aren't usually covered during an introduction to abstract algebra.

1) While the modern upper-level undergraduate curriculum does push a lot more abstraction than appeared a century ago, this is still balanced with the psychological need for students to not go up too many levels too quickly. Even though categories are some kind of algebraic structure generalizing groups and lattices, the standard examples are categories of other mathematical objects one has already studed (sets, groups, etc.). For students this is conceptually quite different from the more concrete situation of finite symmetry groups, for example.

2) The applications of categories (separately from the special cases of groups/lattices/monoids/posets/etc.) don't yet appear enough for the average person with a bachelor's in math to need to know them. This may change as #AppliedCategoryTheory, #TopologicalDataAnalysis, #FunctionalProgramming, and so forth continue to mature and have greater impacts outside of academia.