The n-Category Café - University of Texas at Austin
网页2024年9月15日 · Earlier on the n -Café, I once outlined a simple proof of Stirling’s formula using Laplace’s method. When I started thinking about statistical mechanics, I got interested in an alternative proof using the Central Limit Theorem, mentioned in a comment by Mark Meckes. Now I want to dramatize that proof using energy particles.
Galois Theory | The n-Category Café - University of Texas at Austin
网页2024年8月15日 · 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.
Axiomatic Set Theory 1: Introduction | The n-Category Café
网页13 小时之前 · Axiomatic Set Theory 1: Introduction. Posted by Tom Leinster. I’m teaching Edinburgh’s undergraduate Axiomatic Set Theory course, and the axioms we’re using are Lawvere’s Elementary Theory of the Category of Sets — with the twist that everything’s going to be done directly in terms of sets and functions, without invoking categories ...
Topos Theory and Measurability | The n-Category Café
网页2021年7月28日 · There was an interesting talk that took place at the Topos Institute recently – Topos theory and measurability – by Asgar Jamneshan, bringing category theory to bear on measure theory. Jamneshan has been working with Terry Tao on this: Asgar Jamneshan, Terence Tao, Foundational aspects of uncountable measure theory: Gelfand duality, Riesz representation, canonical models, and canonical ...
Compositional Thermostatics (Part 1) | The n-Category Café
网页2021年11月23日 · 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 …
The n-Category Café
网页2024年8月31日 · Earlier on the n -Café, I once outlined a simple proof of Stirling’s formula using Laplace’s method. When I started thinking about statistical mechanics, I got interested in an alternative proof using the Central Limit Theorem, mentioned in a comment by Mark Meckes. Now I want to dramatize that proof using energy particles.
Grothendieck--Galois--Brauer Theory (Part 1) | The n-Category Café
网页2023年6月26日 · Grothendieck’s Galois theory. In 1960 and 1961 Grothendieck developed a new approach to Galois theory in a series of seminars that got written up as SGA1. This is sometimes called Grothendieck’s Galois theory. His approach was very geometrical. He treated the Galois group of a field k as the fundamental group of a funny sort of ‘space ...
August 2021 Archives | The n-Category Café - University of Texas …
网页2021年8月3日 · One of the most curious things about formal treatments of type theory is the attention paid to dummy variables. The point is simple enough to explain to a calculus student: just as the integrals ∫ 0 2 x 3 dx \int_0^2 x^3 \, dx and ∫ 0 2 t 3 dt \int_0^2 t^3 \, dt are equal, so are the functions λ x. x 3 \lambda x. x^3 and λ t. t 3 \lambda t. t^3 — the name of the variable doesn’t matter.
June 2021 Archives | The n-Category Café - University of Texas at …
网页2021年6月29日 · The dual transport problem from general linear programming duality. Last time I described the basic, discrete optimal transport problem in which there are some suppliers wanting to supply certain amounts of some resource (eg loaves of bread) and some receivers wanting to receive a certain amount of that resource. There’s a cost associated to transporting a unit of the resource from a ...
Modal Homotopy Type Theory - The Book | The n-Category Café
网页2020年2月6日 · modalities (by which I mean: factorization systems on ∞ \infty-categories with base-change-stable left class – I’m not 100% this is the sense the term is being used in the present context).. Yes, that’s correct, modulo internalization. A modality in the internal homotopy type theory of a locally cartesian closed ∞ \infty-category corresponds externally to a pullback-stable ...