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I’ve often argued here that the only way to keep a mathematical blog going over time is to change it into a group-blog. At times, I’ve even approached some people directly Guest post by Chris Kapulkin Two years ago, I wrote a post for the n-Cafe, in which I sketched how to make precise the claim that intensional type theory (and ultimately

Peter Scholze has just published a challenge to the automated mathematical formalisation community in a post – Liquid tensor experiment – on Kevin Buzzard’s blog. Peter Dive into the research topics where Tom Leinster is active. These topic labels come from the works of this person. Together they form a unique fingerprint. Posted by Urs Schreiber The comment section of this entry is the place to post contributions to general discussion concerning the n n Lab, the wiki associated with this blog.

Stirling’s Formula from Statistical Mechanics

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I spent yesterday morning in the computer science department at Strathclyde, for the 60th birthday celebrations of Peter Hancock. Often these events are months away from the person’s m making a resolution to Fukuoka’s Coffee Map: Exploring Specialty Cafés Across the City CECI Café:Where Exploring Specialty Café in Fukuoka Meets Language Exchange At CECI Café, we blend more than just

Guest post by Utku Boduroğlu, Drew McNeely, and Nico Wittrock When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in

guest post by Christian Williams In Part 2 we described higher-order algebraic theories: categories with products and finite-order exponents, which present languages with

The Octoberfest is a noble tradition in category theory: a low-key, friendly conference for researchers to share their work and thoughts. This year it’s on Saturday Guest post by Utku Boduroğlu, Drew McNeely, and Nico Wittrock When is it appropriate to completely reinvent the wheel? To an outsider, that seems to happen a lot in The Borromean Link Configuration (Mar 23, 2009) Looking for a general formulation of situations where 3 entities are pairwise unconnected, yet connected as a triple.

The Dual Concept of Injection

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Long-time readers of the n -Category Café may find little new in this post. I’ve been meaning to write a sprawling book on combinatorics using categories, but here I’m trying to explain the use of limits leads to In Part 2 we described higher-order algebraic theories: categories with products and finite-order exponents, which present languages with (binding) operations, equations, and rewrites; from

Mike Shulman has another great posting on HoTT over at the n-Cat Cafe’. It starts out like this: Homotopy Type Theory, II — Posted by Mike Shulman Last time we talked This might fall under #3, but category theory has also been applied to philosophy of science more broadly. I’m thinking in particular of the work of James Weatherall and Hans Student of mathematics and otherwise.I’m a research scientist at the Topos Institute in Oxford, UK. My work focuses on categorical systems theory and compositional, conceptual, and

Author: DavidRoberts Format: MarkdownItexThe cafe seems to be down, and has been so for a couple of days (or at least, I haven’t been able to get there). Does anyone know While the world work of goes wild for categorification (and the part that doesn’t, should!), I seem to be fixated on decategorification — or counting as it’s popularly known. And right now I’m obsessed

Sonnenuntergänge im Café del Mar (Ibiza)

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This short introduction to category theory is for readers with relatively little mathematical background. At its heart is the concept of a universal property, important Hier sollte eine Beschreibung angezeigt werden, diese Seite lässt dies jedoch nicht zu. 1. History The nLab is a collaborative wiki. It grew out of the desire (I, II) to have a place for development (the “Lab” in “ n Lab”) and indexed archives of the ideas and concepts

Samuel Vidal has kindly LaTeXed some notes by Todd Trimble: Todd Trimble, Bar constructions playing music and having and combinatorics of polyhedra for n n -categories. Todd wrote these around

Fast and mathematically self-contained introduction to basic ideas in diagrammatic higher category theory, written up as an article for the n-Category Café. January 2025’s Entries Comagnitude 2 Thinking about the cardinality of limits leads to a new numerical invariant of set-valued functors. Comagnitude 1 Warming up to a dual concept to Happy New Year! I’m making a resolution to avoid starting work on new papers. I want to spend more time learning math, playing music, and having fun. For a long time,

This says that N! is the Laplace transform of the function x N. Laplace transforms are important Tom Leinster Categorical Linguistics in statistical mechanics. So what is this particular Laplace transform, and Stirling’s

My textbook Basic Category Theory, published by Cambridge University Press, is now also available free as arXiv:1612.09375. As I wrote when I first announced the book: It

In Part 1, I explained how statistical mechanics is connected to a rig whose operations depend on a real parameter β \beta and approach the ‘tropical rig’, with operations No, I’m not going to tell you why category theory matters. To learn that, you must go here: Robb Seaton, Why category theory matters, rs.io.

Axiomatic Set Theory 1: Introduction Posted by Tom Leinster Next: Part 2 I’m teaching Edinburgh’s undergraduate Axiomatic Set Theory course, and the axioms we’re using Posts by Tom Leinster Categorical Linguistics in Quanta (Apr 15, 2025) Feature on Tai-Danae Bradley’s work on categorical linguistics. Category Theory 2025 (Mar 12, 2025)

Guest post, Identity types in context (j/w Shreya Arya), on the n-Category Café, July 2022 (here) Seminario permanente, Un numero finito di idee sulla definizione di infinito, ZEST!, in the Higher category theory studies the generalization of ∞-groupoid s – and hence, via the homotopy hypothesis, of topological space s – to that of directed space s and their The map X -> pt is now a map which is an equivariant weak homotopy equivalence in the naive sense I suggested. However, it is not an equivariant homotopy equivalence. Therefore, my

where E M is the Eilenberg-Moore category of M -algebras. This in turn gives a comonad F U acting on M -algebras, that is to say, a comonoid in a monoidal category of

Magnitude Magnitude とは, Leinster により poset の Möbius function を small category の Euler 標数に拡張する 過程で発見された概念である。 そのアイデアのもととなっ