The n-Category Café - University of Texas at Austin
WEB5 days ago · 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.
How to Apply Category Theory to Thermodynamics
WEBJul 25, 2022 · The functor Ent: ConvRel → Set is defined as follows: For convex space A, Ent(A) takes A to the set of entropy functions on A, which is a an object in Set. For morphism R: A → B, Ent[R] is a morphism Ent[R]: Ent(A) → Ent(B). For entropy function S: A → ˉℝ, we define. Ent[R](S)(p) = sup {a | (a, p) ∈ R} S(a).
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.
Axiomatic Set Theory 1: Introduction | The n-Category Café
WEB4 days ago · Re: Axiomatic Set Theory 1: Introduction. In page 12 of your notes you write, “Every calculus book defines a sequence as a function with domain N \mathbb {N}. Now, we don’t usually think of sequences as functions, and that’s reflected in the notation. No one says ‘let f f be a sequence’; we say ‘let (xn)∞ n=0 (x_n)_ {n=0}^\infty ...
Algebraic Closure | The n-Category Café - University of Texas at …
WEBApr 13, 2021 · The algebraic closure of a field is the choice of a point of a suitable topos associated to the field. Given a topos there is canonically given category of points of the topos, but there is no reason why a specific point would be better than any other, even when the category of points is a connected non empty groupoid.
Large Sets 13 | The n-Category Café - golem.ph.utexas.edu
WEBJul 22, 2021 · Large Sets 13. Posted by Tom Leinster. Previously: Part 12.5. This is the last post in the series, and it’s a short summary of everything we’ve done. Part 1: introduction. Part 2: limits. Part 3: well-ordered sets. Part 4: the index of a set. Part 5: alephs.
The n-Category Café
WEBAug 31, 2024 · 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.
The Categorical Origins of Lebesgue Integration, Revisited
WEBNovember 11, 2020. The Categorical Origins of Lebesgue Integration, Revisited. Posted by Tom Leinster. I’ve just arXived a new paper: The categorical origins of Lebesgue integration (arXiv:2011.00412). Longtime Café readers may remember that I blogged about this stuff back in 2014, but I’ve only just written it up.
Topos Theory and Measurability | The n-Category Café
WEBJul 28, 2021 · 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 ...
This Week's Finds (1--50) | The n-Category Café - University of …
WEBJan 12, 2021 · Take a copy of this! • This Week’s Finds in Mathematical Physics (1-50), 242 pages. These are the first 50 issues of This Week’s Finds of Mathematical Physics.This series has sometimes been called the world’s first blog, though it was originally posted on a “usenet newsgroup” called sci.physics.research — a form of communication that predated the world-wide web.
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