Understanding the Homotopy Coherent Nerve | The n-Category Café
WEBApr 29, 2010 · I was really happy to understand this construction, both the fact that ℂ \mathbb{C} on categories (and in particular, on Δ \Delta) coincides with the comonad resolution, and the resulting description of the coherent nerve.The definition of the coherent nerve you sometimes read, by first defining the homset of ℂ [n] \mathbb{C}[n] as the nerve of some random poset, always made it seem very ...
itex2MML - University of Texas at Austin
WEBJan 2, 2019 · The resulting itex2MML binary is a stream filter. It takes text with embedded itex equations on STDIN, converts the itex equations to MathML, and outputs the resulting text on STDOUT. Also included are Ruby bindings. The easiest way to obtain them, with a recent version of Rubygems is. gem install itextomml.
Dimensional Analysis in Algebra and Geometry | The n-Category …
WEBAug 8, 2024 · They will take a polynomial equation like. y = 3 x 2 + 4 x y = 3x^2 + 4 x. and use Descartes’ trick to make the dimensions match up. Suppose x x and y y have units of length. Then they let z z stand for 1 meter, and rewrite the equation as. y …
Exact Squares | The n-Category Café - University of Texas at Austin
WEBJun 21, 2010 · In order to get used to the calculus of exact squares, the first thing we have to change is to start thinking more in terms of Kan extensions rather than limits and colimits.For instance, it’s usual to think of a pullback as the limit of a diagram of shape B → C ← A B \to C \leftarrow A (a cospan) i.e. an object P P equipped with a natural transformation of cospans: P → P ← P ↓ ↓ ...
The Space of Physical Frameworks (Part 2) | The n-Category Café
WEBSep 7, 2024 · The maximum value of S(E) − CE is called free entropy and denoted Φ. In short: Φ(C) = sup E (S(E) − CE) or if you prefer. −Φ(C) = inf E (CE − S(E)) This way of defining −Φ in terms of S is called a Legendre–Fenchel transform, though conventions vary about the precise definition of this transform, and also its name.
2-Toposes | The n-Category Café - University of Texas at Austin
WEBJan 12, 2008 · As 2-toposes seem to be cropping up a bit, here and here, let’s see if we can attract some experts to teach us about them. On p. 36 of Mark Weber’s Strict 2-toposes, a 2-topos is defined as a finitely complete cartesian closed 2-category equipped with a duality involution and a classifying discrete opfibration.Cat is a good example of a 2-topos. Are there other familiar one
Proof by Coinduction | The n-Category Café - University of Texas …
WEBSep 18, 2009 · Proof by Coinduction. Posted by David Corfield. The sophisticated take on mathematical induction is that the natural numbers form the inital algebra of the endofunctor on Set, F: X → 1 + X. As such we have a map 0, s : 1 + ℕ → ℕ, picking out the zero and the successor function. As an initial object in the category of F -algebras we know ...
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.
In Praise of the Gershgorin Disc Theorem | The n-Category Café
WEBAug 9, 2016 · Sometimes called “Gershgorin’s Circle Theorem” Right — lots of people do call it that. But mathematicians settled long ago on using “circle” for the hollow shape and “disc” for the solid shape, and the actual circles play no particular role in Gershgorin’s theorem; it’s the discs that matter. So I prefer the name “Gershgorin disc theorem”.
The n-Category Café - University of Texas at Austin
WEB6 days ago · 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.