John C. Baez's Blog, page 47

Topos Theory (Part 2)

Last time I defined sheaves on a topological space this time I’ll say how to get these sheaves from ‘bundles’ over You may or may not have heard of bundles of various kinds, like vector bundles or fiber bundles. If you have, be glad: the bundles I’m talking about now include these as special cases. If not, don’t worry: the bundles I’m talking about now are much simpler!

A bundle over is simply a topological space equipped with a continuous map to say

You should visualize as hovering...

Topos Theory (Part 1)

I’m teaching an introduction to topos theory this quarter, loosely based on Mac Lane and Moerdijk’s Sheaves in Geometry and Logic.

I’m teaching one and a half hours each week for 10 weeks, so we probably won’t make it far very through this 629-page book. I may continue for the next quarter, but still, to make good progress I’ll have to do various things.

First, I’ll assume basic knowledge of category theory, a lot of which is explained in the Categorical Preliminaries and Chapter 1 of this...

Schrödinger and Einstein

Schrödinger and Einstein helped invent quantum mechanics. But they didn’t really believe in its implications for the structure of reality, so in their later years they couldn’t get themselves to simply use it like most of their colleagues. Thus, they were largely sidelined. While others made rapid progress in atomic, nuclear and particle physics, they spent a lot of energy criticizing and analyzing quantum theory.

They also spent a lot of time on ‘unified field theories’: theories that...

Compositionality — First Issue

[image error]

Yay! The first volume of Compositionality has been published! You can read it here:

https://compositionality-journal.org

“Compositionality” is about how complex things can be assembled out of simpler parts. Compositionality is a journal for research using compositional ideas, most notably of a category-theoretic origin, in any discipline. Example areas include but are not limited to: computation, logic, physics, chemistry, engineering, linguistics, and cognition.

Compositionality is a...

How to Solve Climate Change

Happy New Year!

This podcast of an interview with Saul Griffith is a great way to start your year:

• Ezra Klein, How to solve climate change and make life more awesome.

Skip straight down to the bottom and listen to the interview! I usually prefer reading stuff, but this is only available in audio form—and it’s worth it.

One important thing he says:

We have not had anyone stand up and espouse a vision of the future that could sound like success.

I think it’s time to start doing that. I...

Applied Category Theory 2020 — Adjoint School

Like last year and the year before, there will be a school associated to this year’s conference on applied category theory! If you’re trying to get into applied category theory, this is the best possible way.

• Applied Category Theory 2020 — Adjoint School.

The school will consist of online meetings from February to June 2020, followed by a research week June 29–July 3, 2020 at MIT in Cambridge Massachusetts. The conference follows on July 6–10, 2020, and if you attend the school you should...

Applied Category Theory Postdocs at NIST

An advertisement:

We are looking to expand our group of applied category theorists at the National Institute of Standards and Technology (NIST). Our group develops use cases, tools and methodology to apply category theory and related methods in a broad range of disciplines centered around the design, implementation, operation and evolution of engineered systems.

We encourage those eligible and interested to apply for the National Research Council Research Associateship Program. The upcoming...

Applied Category Theory Meeting at UCR (Part 3)

 

We had a special session on applied category theory here at UCR:

• Applied category theory, Fall Western Sectional Meeting of the AMS, 9–10 November 2019, U.C. Riverside.

I was bowled over by the large number of cool ideas. I’ll have to blog about some of them. A bunch of people stayed for a few days afterwards, and we had lots of great conversations.

The biggest news was that Brendan Fong and David Spivak definitely want to set up an applied category theory in the San Francisco Bay Area, which they’re calling the Topos Institute. T...

Why Is Category Theory a Trending Topic?

I wrote something for the Spanish newspaper El País, which has a column on mathematics called “Café y Teoremas”. Ágata Timón helped me a lot with writing this, and she also translated it into Spanish:

• John Baez, Qué es la teoría de categorías y cómo se ha convertido en tendencia, El País, 8 November 2019.

Here’s the English-language version I wrote. It’s for a general audience so don’t expect hard-core math!

Why has “category theory” become a trending topic?

Recently, various scientific media have been paying attention to a branch of mathematics...

Diversity Workshop at UCR

I’m organizing a workshop to promote diversity in math here at UCR:

• Riverside Mathematics Workshop for Excellence and Diversity, Friday 8 November 2019, U. C. Riverside.

It’s right before the applied category theory meeting, so I hope some of you can make both… especially since the category theorist Eugenia Cheng will be giving a talk!

Three talks will take place in Skye Hall—home of the math department—starting at 1 pm. After this we’ll have refreshments and an hour for students to talk t...