The n-Category Café - University of Texas at Austin
WEBSep 15, 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.
New Normed Division Algebra Found! | The n-Category Café
WEBSep 23, 2020 · New Normed Division Algebra Found! Posted by John Baez. Hurwitz’s theorem says that there are only 4 normed division algebras over the real numbers, up to isomorphism: the real numbers, the complex numbers, the quaternions, and the octonions. The proof was published in 1923. It’s a famous result, and several other proofs are known.
The Behavioral Approach to Systems Theory | The n-Category Café
WEBJun 15, 2018 · guest post by Eliana Lorch and Joshua Tan. As part of the Applied Category Theory seminar, we discussed an article commonly cited as an inspiration by many papers 1 taking a categorical approach to systems theory, The Behavioral Approach to Open and Interconnected Systems.In this sprawling monograph for the IEEE Control Systems Magazine, legendary control theorist Jan Willems poses and answers ...
Lurie on TQFT and the Cobordism Hypothesis
WEBFeb 13, 2009 · David Ben-Zvi notes that we can now see these talks by Jacob Lurie: Jacob Lurie, TQFT and the cobordism hypothesis, videos of 4 lectures at the Geometry Research Group, Mathematics Department, University of Texas Austin. Lecture notes should be forthcoming. For a brief summary of the cobordism hypothesis and …
Australian Category Theory | The n-Category Café - University of …
WEBOct 18, 2006 · Here are some more talks: Ross Street, Kan extensions in basic group representation theory.Wednesday November 1, 2006. Dorette Pronk, Conformal field theory as a nuclear functor.(Joint work with Prakash Panangaden and Rick Blute.)Wednesday November 1, 2006. Abstract: Segal’s definition of a conformal field theory discusses “functors” for which the domain is not a category.
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.
Classical Dualities and Formal Concept Analysis
WEBSep 12, 2013 · Similarly, we have 𝒫cl(M) — in formal concept analysis these are called the intents. The Galois connection restricts to a Galois correspondence, i.e. a duality, between the closed subsets of G and the closed subsets of M . I *: 𝒫cl(G) ≅ 𝒫cl(M)op: I *. The concepts are then pairs (A, B) consisting of a closed subset of G and the ...
Inner Automorphisms of the Octonions | The n-Category Café
WEBNov 22, 2022 · Does he describe the other conjugacy class of order 3 automorphisms? (There are exactly two, and only one class of order 2s.) At the far end of the Weyl alcove, i.e. the conjugate points of the exponential map from the Lie algebra to the compact group, there’s an 11-dim family of automorphisms that includes the C-based and H-based ones we were discussing, at the two ends.
The Two Cultures Again | The n-Category Café - University of …
WEB1. closed conditions. These are conditions that generally involve an = = or a ≥ \ge sign or the universal quantifier, and thus codify such things as algebraic structure, non-negativity, non-strict monotonicity, semi-definiteness, etc. As the name suggests, such conditions tend to be closed with respect to limits and morphisms. 2. open conditions.
Symmetric Monoidal Bicategories | The n-Category Café
WEBOct 4, 2012 · A Picard 2-category is a symmetric monoidal bicategory in which every 2-cell is invertible, every 1-cell is an equivalence, and every object has a tensor inverse (up to equivalence). It is a kind of twice-categorified version of an abelian group. Our coherence theorem, as well as the construction of the E∞. E ∞.
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