Tootfinder

Temperley-Lieb Categories on Non-Orientable Surfaces
Dionne Ibarra, Gabriel Montoya-Vega, Benjamin Morris
https://arxiv.org/abs/2506.14319 https://

Temperley-Lieb Categories on Non-Orientable Surfaces
In this paper we present the construction of a skeletal diagram category, which we call the square with bands category. This category extends the Temperley-Lieb (TL) category, where morphisms now include diagrams of embedded curves on (possibly) non-orientable bounded surfaces, and involves three parameters associated to simple closed curves. Such diagrams utilise handle decompositions for surfaces and are considered up to a handle slide equivalence. We define a tensor product on this category,…

Monotone weak distributive laws over the lifted powerset monad in categories of algebras
Quentin Aristote (UPCit\'e, IRIF, PICUBE)
https://arxiv.org/abs/2507.13058

Monotone weak distributive laws over the lifted powerset monad in categories of algebras
Noticing the similarity between the monotone weak distributive laws combining two layers of nondeterminism in sets and in compact Hausdorff spaces, we study whether the latter law can be obtained automatically as a weak lifting of the former. This holds partially, but does not generalize to other categories of algebras: we then characterize when exactly monotone weak distributive laws over powerset monads in categories of algebras exist, exhibiting a law combining probabilities and non-determin…

arxiv_collab: Scientific collaborations in physics (1995-2005)
Collaboration graphs for scientists, extracted from the Los Alamos e-Print arXiv (physics), for 1995-1999 for three categories, and additionally for 1995-2003 and 1995-2005 for one category. For copyright reasons, the MEDLINE (biomedical research) and NCSTRL (computer science) collaboration graphs from this paper are not publicly available.
This network has 8361 nodes and 15751 edges.
Tags: Social, Collaboration…

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

iPadOS 26 & Co.: Endlich festlegen, welche Apps welche Dateien öffnen
Apples Dateien-App wird auf iPhone und iPad endlich mächtiger. Die Vorschau-App kommt auch aufs iPhone.
https://www.

This Github repository conveniently lists and categorizes prime examples of LLM-based agent applications. Each example application features its own repository folder with its source code (Python), and a helpful README.md file describing its installation and use.
Categories include:
1. Starter AI Agents
2. Advanced AI Agents
3. Autonomous Game Playing Agents
4. Multi-Agent Teams
5. Voice AI Agents
6. RAG-Based Agents
"awesome-llm-apps"

'Tariff engineering' is making a comeback as businesses employ creative ways to skirt higher duties (Anniek Bao/CNBC)
https://www.cnbc.com/2025/06/18/businesses-tweak-products-to-qualify-for-lowter-tariffed-categories-.html
http://www.memeorandum.com/250618/p34#a250618p34

Integration of a categorical operad
Dominik Trnka
https://arxiv.org/abs/2506.12399 https://arxiv.org/pdf/2506.12399

Integration of a categorical operad
I describe Grothendieck construction for non-symmetric operads with values in categories, and hence in groupoids and posets. The construction produces a 2-category which is operadicaly fibered over the category $Δ_s$ of finite non-empty ordinals and surjections. I describe an inverse for the construction, yielding a 1-1 correspondence of non-symmetric categorical operads and operadic 2-categories (split-)fibered over $Δ_s$, which resembles the correspondence of categorical presheaves and fibe…

On the LIME Energy Saving Plug: Review (2011) - Read how this simple helpful gadget chopped the watts to save cash and carbon! #smartPlug #frugal #cutCarbon -

On the LIME Energy Saving Plug: Review (2011)
Read how this simple helpful gadget chopped the watts to save cash and carbon! #smartPlug #frugal #cutCarbon

On pure monomorphisms and pure epimorphisms in accessible categories
Leonid Positselski
https://arxiv.org/abs/2506.13374 https://arxi…

On pure monomorphisms and pure epimorphisms in accessible categories
In all $κ$-accessible additive categories, $κ$-pure monomorphisms and $κ$-pure epimorphisms are well-behaved, as shown in our previous paper arXiv:2311.02418. This is known to be not always true in $κ$-accessible nonadditive categories. Nevertheless, mild assumptions on a $κ$-accessible category are sufficient to prove good properties of $κ$-pure monomorphisms and $κ$-pure epimorphisms. In particular, in a $κ$-accessible category with finite products, all $κ$-pure monomorphisms are $κ…