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.
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 ...
Australian Category Theory | The n-Category Café - University of …
WEBOct 18, 2006 · Ross Street, An Australian conspectus of higher category theory, to appear in the proceedings of n-Categories: Foundations and Applications, eds. J. Baez and P. May. For example, check out the fun story on page 4 where an Australian student, asked if he knew the definition of a topological space, correctly but incomprehensibly replied:
Hoàng Xuân Sính | The n-Category Café - University of Texas at …
WEBJun 20, 2022 · Hoàng Xuân Sính was born in 1933 in a village called Cót, one of seven children of a fabric merchant. Her mother died when she was eight years old, and she was raised by a stepmother. She spent a lot of time . But apparently her father pushed her to excel academically.
More Secrets of the Associahedra | The n-Category Café
WEBJan 25, 2018 · Looks like Proposition 13.11.7 of Loday and Valette’s book Algebraic Operads gives the same argument. Maybe it’s be more geometrically suggestive to interpret the associahedron as the “moduli space of metric planar graphs”, and the “bar construction” as computing the cohomology of a constructible sheaf on this space using the canonical CW-structure. Ginzburg and Kapranov do the ...
The Algebraic K-Theory of the Integers | The n-Category Café
WEBDec 9, 2020 · The algebraic K K-groups of the integers, and other rings, are a big deal.A lot of fairly recent progress on understanding them is due to Voevodsky, Rost, Rognes and Weibel, whose work culminated in a proof of the Bloch–Kato Conjecture connecting K K-theory to Galois cohomology.But lots of other mathematicians deserve credit too.
Octonions and the Standard Model (Part 2) | The n-Category Café
WEBJul 23, 2020 · The payoff for all these contortions is a very pretty formula for octonion multiplication. We’ll take elements of ℂ ⊕ ℂ3 and write them like a + →a, where the ‘scalar part’ a lives in ℂ and the ‘vector part’ →a lives in ℂ3. And these will be our octonions! Theorem 2. If we define multiplication on ℂ ⊕ ℂ3 by.
Weakly Globular Double Categories: a Model for Bicategories
WEBSep 27, 2021 · This will enable us to develop a model of bicategories that lives between strict 2-categories and double categories. Two facts are going to help us develop this model: Fact 1. X ∈ [Δop, Cat] is the horizontal nerve of a double category iff the Segal maps ηk: Xk → X1 ×X0k ⋯ ×X0X1 are isomorphisms. Fact 2. X ∈ [Δop, Cat] is the nerve ...
100 Papers on Magnitude | The n-Category Café - University of …
WEBJun 14, 2024 · A milestone! By my count, there are now 100 papers on magnitude, including several theses, by a total of 73 authors.You can find them all at the magnitude bibliography.. Here I’ll quickly do two things: tell you about some of the hotspots of current activity, then — more importantly — describe several regions of magnitude-world that haven’t received the attention they could have, and ...
Category Theoretic Modal Logic | The n-Category Café
WEBApr 4, 2011 · In one form of these, typed classical first-order hyperdoctrines, we have a functor from Bop to BA with certain properties, where B is a category with finite products corresponding to the types of the theory. The extension to modal logic should then involve a modal hyperdoctrine, a functor Bop to MA, the category of modal algebras.