### This Week’s Finds (51–100)

#### Posted by John Baez

Grab a copy of this:

These are the second fifty issues of my column, from April 23, 1995 to March 23, 1997. They discuss quantum gravity, topological quantum field theory and other topics in mathematics and physics. They were typeset in 2020 by Tim Hosgood. Since then I’ve edited them more and changed most references to preprints into references to published papers and/or the arXiv. If you see typos or other problems please report them. (I already know the cover page looks weird).

By the way, I’ve also done a lot more editing of the first 50 issues, with help from Fridrich Valach, so please grab a new copy of this even if you already have it:

*This Week’s Finds in Mathematical Physics (1–50)*, 241 pages.

But let me say a bit more about what’s in issues 51–100.

Weeks 50–100 contain two long expository threads. One is on “ADE classifications”:

Week 62 — The ubiquity of ADE classifications. The classification of finite reflection groups using Coxeter diagrams.

Week 63 — The classification of crystallographic finite reflection groups and semisimple Lie algebras.

Week 64 — Semisimple Lie algebras. Affine Lie algebras, Wess–Zumino–Witten models and quantum groups.

Week 65 — The A, D, and E lattices. The McKay correspondence and the classification of minimal models.

The other, called the “The Tale of $n$-Categories”, was an introduction to categories and higher categories — mainly just 2-categories. It can be found in these issues:

Week 73 — The category of sets and the 2-category of categories.

Week 74 — Kinds of categories: monoids, groups, and groupoids. The periodic table of $n$-categories.

Week 75 — The fundamental groupoid of a topological space. The classifying space of a groupoid.

Week 76 — Equations, isomorphisms, and equivalences. Adjoint functors.

Week 77 — Adjoint functors.

Week 78 — Adjoint functors and adjoint linear operators.

Week 79 — The unit and counit of an adjunction.

Week 80 — The definition of 2-category.

Week 83 — Adjunctions in 2-categories and dual objects in monoidal categories.

Week 84 — Review. Monads and monoids.

Week 89 — Monads in 2-categories. Monoids and monoidal categories as monads.

Week 92 — Monads from adjunctions.

Week 99 — 2-Hilbert spaces. Coproducts.

Week 100 — Definitions of $n$-category.

I am now editing issues 101–150, which total 347 pages. In old age I am paying penance for the loquacity of youth.

## Re: This Week’s Finds (51–100)

Wow, do those take me back. Around week 62 or so is when I started college and first had an internet connection. I’m not sure exactly when after that I discovered sci.math and sci.physics and started reading This Week’s Finds regularly, but it was probably within the first year. There was obviously a lot in there that I wasn’t prepared to understand (and there still is!), but I fondly remember TWF as giving me my first glimpse into just how big mathematics is.