Tootfinder

The familial nature of enrichment over virtual double categories
Soichiro Fujii, Stephen Lack
https://arxiv.org/abs/2507.05529 https://

The familial nature of enrichment over virtual double categories
Originally enriched categories were defined over a monoidal category, but it was gradually realized that important examples can only be included when one enriches over more general structures such as bicategories and virtual double categories. We show that, as well as allowing more examples, working over virtual double categories also gives better formal properties. We study the 2-functor sending a virtual double category to the 2-category of categories enriched over it. We show that this is a …

Quand la souveraineté digitale fait bouger des plaques tectoniques
Japon - EU
Sans parler de la Chine, avec plusieurs années d’avance sur la question https://altstack.jp/en/categories/

A Categorical Perspective on Braid Representations
P. P. Martin, E. C. Rowell, F. Torzewska
https://arxiv.org/abs/2506.07950 https://…

A Categorical Perspective on Braid Representations
We study categories whose objects are the braid representations, that is, strict monoidal functors from the braid category $B$ to the category of matrices $Mat$. Braid representations are equivalent to solutions to the (constant) Yang-Baxter equation. So their classification problems are also equivalent. We consider both the categories $MoonFun(B,Mat)$ whose morphisms are natural transformations and the category $MonFun(B,Mat)$ whose morphisms are the monoidal natural transformations. This cate…

@… @ethicalrevolution I see you share reviews from other websites, so wondering if mine might qualify. Thanks for your efforts for unsigned musicians. https://muz4now.com/category/biz/unsig

Unsigned Musicians Archives

Slept through it. Catch-up couldn't go beyond 2 AM (#WWDC25 was at 1 AM SGT) because reached the 800 limit on Mastodon 🤦‍♂️
Maybe Mastodon should limit it by time duration or something instead.

Saving Electricity and Gas - Avoiding 6 tonnes of CO2 per year at home! #electricity #fossilGas #cutCarbon -

Saving Electricity and Gas
Avoiding 6 tonnes of CO2 per year at home! #electricity #fossilGas #cutCarbon

The compact double category $\mathbf{Int}(\mathbf{Poly}_*)$ models control flow and data transformations
Grigory Kondyrev, David I. Spivak
https://arxiv.org/abs/2509.05462 https…

The compact double category $\mathbf{Int}(\mathbf{Poly}_*)$ models control flow and data transformations
Hasegawa showed that control flow in programming languages -- while loops and if-then-else statements -- can be modeled using traced cocartesian categories, such as the category $\mathbf{Set}_*$ of pointed sets. In this paper we define an operad $\mathscr{W}$ of wiring diagrams that provides syntax for categories whose control flow moreover includes data transformations, including deleting, duplicating, permuting, and applying pre-specified functions to variables. In the most basic version, the…

Saving Electricity and Gas - Avoiding 6 tonnes of CO2 per year at home! #electricity #fossilGas #cutCarbon -

Saving Electricity and Gas
Avoiding 6 tonnes of CO2 per year at home! #electricity #fossilGas #cutCarbon

Horizontal Descent, Immersions, Unramified Morphisms, Submersions, \'Etale Morphisms and the Relative Cotangent Sequence in Tangent Categories
Jean-Simon Pacaud Lemay, Geoff Vooys
https://arxiv.org/abs/2506.07874

Horizontal Descent, Immersions, Unramified Morphisms, Submersions, Étale Morphisms and the Relative Cotangent Sequence in Tangent Categories
In this paper we provide a deep and systematic study of the classes of what it means to be an immersion, a submersion, a local diffeomorphism, and unramified in a tangent category. We also give a systematic study of the ways in which these classes of morphisms interact, the properties they have, and give very explicit and concrete characterizations of how each class of maps appear in algebraic geometry, in differential geometry, in the theory of semirings, and in the theory of Cartesian differe…

Super-Insulating Our Living Room (2010) - Learn how we retrofitted interior wall insulation for winter warmth and summer cool, and trimmed our carbon footprint. #aerogel #frugal #cutCarbon -

Super-Insulating Our Living Room (2010)
Learn how we retrofitted interior wall insulation for winter warmth and summer cool, and trimmed our carbon footprint. #aerogel #frugal #cutCarbon