Category Theory in Context | The n-Category Café - University of …
WEBNov 17, 2016 · In my final year at Harvard and again in my first year at Johns Hopkins, I had an opportunity to teach an advanced undergraduate/beginning graduate-level topics course entitled “Category Theory in Context.”Its aim was to provide a first introduction to the basic concepts of category theory — categories, functors, natural transformations, the Yoneda lemma, limits and colimits, adjunctions ...
Octonions and the Standard Model (Part 1) | The n-Category Café
WEBJul 17, 2020 · Looking for precedents to this approach, I stumbled upon this old answer on Math StackExchange, though not all the conjugates seem to be in the same places.(There could have been a typo, or I might be missing something.) I’m vaguely disappointed that the term “musical isomorphism” was apparently invented because of the notation, rather than some analogy to esoteric music theory.
Compositional Thermostatics (Part 1) | The n-Category Café
WEBNov 23, 2021 · Compositional Thermostatics (Part 1) Posted by John Baez. At the Topos Institute this summer, a group of folks started talking about thermodynamics and category theory. It probably started because Spencer Breiner and my former student Joe Moeller, both working at the National Institute of Standards and Technology, were talking about ...
The Quintic, the Icosahedron, and Elliptic Curves
WEBApr 18, 2024 · There is a remarkable relationship between the roots of a quintic polynomial, the icosahedron, and elliptic curves. This discovery is principally due to Felix Klein (1878), but Klein’s marvellous book misses a trick or two, and doesn’t tell the whole story. The purpose of this article is to present this relationship in a fresh, engaging ...
Not Even Wrong | The String Coffee Table - University of Texas at …
WEBAug 19, 2006 · Not Even Wrong. Posted by Aaron. The physics blog-wars have hit the world of publishing with Peter Woit ’s Not Even Wrong and Lee Smolin ’s The Trouble with Physics. Having given up blogging long ago, I still seem to have spent an inordinate amount of time in these internet trenches. Since Dr. Woit was kind enough to send me a …
Learn Applied Category Theory! | The n-Category Café
WEBOct 28, 2021 · Mathematical Research Community: Applied Category Theory, meeting 2022 May 29–June 4. Details on how to apply: here. Deadline to apply: Tuesday 2022 February 15 at 11:59 Eastern Time. After working with your team online, you’ll take an all-expenses-paid trip to a conference center in upstate New York for a week in the summer.
Three Phases of Continued Fraction Theory | The n-Category Café
WEBSep 6, 2020 · But in all these cases we actually get much more: we get continued fraction expansions for the functions ln z \ln z, arctan z \arctan z and e z e^z — and making the right choice of z z we get our formulas for ln 2 \ln 2, 4 / π 4/\pi and e e, respectively. Indeed Euler’s formula gives nice continued fractions for all functions with simple ...
Quantum Computation and Symmetric Monoidal Categories | The …
WEBRe: Quantum computation and symmetric monoidal categories. Concerning Frobenius algebras, one can actually drop the additional biproduct structure used in A categorical semantics of quantum protocols and encode classical data manipulations using dagger-compact Frobenius algebras, while, crucially, seemingly retaining all required expressive power. In Quantum measurements without sums Dusko ...
Galois Theory | The n-Category Café - University of Texas at Austin
WEBAug 15, 2024 · About 40 short explanatory videos. A large collection of problems. Nearly 500 multiple choice questions. I’m a little bemused by the popularity of the Galois theory notes. I’ve made quite a few sets of course notes public before, e.g.: Fourier analysis. General topology. Linear algebra. Category theory.
Tangent ∞-Categories and Cohesion | The n-Category Café
WEBFeb 2, 2021 · For clarity, I will use the following terminology in this post: A Rosicky tangent category is a tangent category in the sense I discussed above – a category C C equipped with an endofunctor T: C → C T: C \to C and so forth. A Rosicky tangent (∞, 1) (\infty,1)-category is the general notion introduced by BBC. “The” tangent category of a differentiable ∞ \infty-category X ∈ Cat ...