The n-Category Café - University of Texas at Austin
网页4 天之前 · Here’s some basic information about the next big annual applied category theory conference — Applied Category Theory 2025 — and the school that goes along with that: the Adjoint School. James Fairbanks will hold ACT2025 and the Adjoint School at the University of Florida, in Gainesville, on these dates: Adjoint School: May 26–30, 2025.
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 3: The Axioms, Part Two
网页3 天之前 · Axiomatic Set Theory 3: The Axioms, Part Two. This week, we finished formulating the axioms of the Elementary Theory of the Category of Sets. 7. For every function f: X → Y. f^ {-1} (y). Category theorists will recognize this as a special case of the existence of pullbacks. But in the presence of the other axioms, this special case alone is ...
Probability Monads as Codensity Monads | The n-Category Café
网页2022年7月19日 · My PhD student Ruben Van Belle has just published his first paper!. Ruben Van Belle, Probability monads as codensity monads. Theory and Applications of Categories 38 (2022), 811–842.. It’s a treasure trove of theorems demonstrating how many of the monads loosely referred to as “probability monads” arise as codensity monads in a certain uniform manner, which I’ll tell you about now.
Compositional Constructions of Automata | The n-Category Café
网页2022年7月28日 · The parallel composite of morphisms A → B → C is defined to be the weighted automaton with states Q × R and whose top and bottom interfaces are the respective set products X × Z and Y × W with sequential interface functions γQ × γR and δQ × δR. The parallel interfaces are A and C with transition matrices defined by.
The Space of Physical Frameworks (Part 5) | The n-Category Café
网页6 天之前 · September 30, 2024. The Space of Physical Frameworks (Part 5) Posted by John Baez. In Part 4, I presented a nifty result supporting my claim that classical statistical mechanics reduces to thermodynamics when Boltzmann’s constant k approaches zero. I used a lot of physics jargon to explain why I care about this result.
Large Sets 6 | The n-Category Café - University of Texas at Austin
网页2021年6月24日 · It seems like there’s no reason to do case analysis on whether ℶ ω \beth_\omega exists in the given model. We can instead say that a set is “small” if it smaller than all cardinals which are ℶ ω \beth_\omega.In general, if we wanted to provide a model of “there are at most n n strong limit cardinals” for some n n, we could just say that a set is “small” if it is smaller ...
Entropy and Diversity Is Out! | The n-Category Café
网页2021年7月25日 · Diversity as the exponential of entropy. The exponential of entropy (Shannon entropy, or more generally Rényi entropy) has long been used by ecologists to quantify biological diversity. One takes a community with n species and writes p = (p1, …, pn) for their relative abundances, so that ∑ pi = 1.
Borel Determinacy Does Not Require Replacement
网页2021年7月23日 · From Martin’s 1975 paper proving the Borel determinacy theorem: Borel determinacy is probably then the first theorem whose statement does not blatantly involve the axiom of replacement but whose proof is known to require the axiom of replacement. From philosopher of mathematics Penelope Maddy (Believing the axioms I, p.490):
Group Cohomology and Homotopy Fixed Points | The n …
网页Theorem. Suppose G G is a group acting strictly on some skeletal category, let a a be an object of that category, and let A = Aut(a) A = \mathrm {Aut} (a) be its automorphism group. Then ways of making a a into a homotopy fixed point of the action of G G correspond bijectively to normalized crossed homomorphisms.