Tootfinder

Applied Category Theory in the Wolfram Language using Categorica I: Diagrams, Functors and Fibrations
Jonathan Gorard
https://arxiv.org/abs/2403.16269 http…

Applied Category Theory in the Wolfram Language using Categorica I: Diagrams, Functors and Fibrations
This article serves as a preliminary introduction to the design of a new, open-source applied and computational category theory framework, named Categorica, built on top of the Wolfram Language. Categorica allows one to configure and manipulate abstract quivers, categories, groupoids, diagrams, functors and natural transformations, and to perform a vast array of automated abstract algebraic computations using (arbitrary combinations of) the above structures; to manipulate and abstractly reason …

A few of the media on my blog in the #Caturday category...
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Omega-categorical pseudofinite groups
Dugald Macpherson, Katrin Tent
https://arxiv.org/abs/2403.17684 https://arxiv.org/pdf/2403.1768…

Omega-categorical pseudofinite groups
We explore the interplay between omega-categoricity and pseudofiniteness for groups, conjecturing that omega-categorical pseudofinite groups are finite-by-abelian-by-finite. We show that the conjecture reduces to nilpotent p-groups of class 2, and give a proof that several of the known examples of omega-categorical p-groups satisfy the conjecture. In particular, we show by a direct counting argument that for any odd prime p the (omega-categorical) model companion of the theory of nilpotent clas…

Regular categories, oligomorphic monoids, and tensor categories
Andrew Snowden
https://arxiv.org/abs/2403.16267 https://arxiv.org/pdf…

Regular categories, oligomorphic monoids, and tensor categories
Knop constructed a tensor category associated to a finitely-powered regular category equipped with a degree function. In recent work with Harman, we constructed a tensor category associated to an oligomorphic group equipped with a measure. In this paper, we explain how Knop's approach fits into our theory. The first, and most important, step describes finitely-powered regular categories in terms of oligomorphic monoids; this may be of independent interest. We go on to examine some aspects of th…

Raiders select versatile pass-catcher with No. 13 pick in draft https://www.yardbarker.com/nfl/articles/raiders_select_versatile_pass_catcher_with_no_13_pick_in_draft/s1_14819_40283256

Raiders select versatile pass-catcher with No. 13 pick in draft
The run on offensive players continues. The Raiders are out of options with respect to quarterbacks, so they have selected Georgia tight end Brock Bowers with the 13th pick. Bowers racked up 2,538 yards and 26 touchdowns during his three-year tenure with the Bulldogs. He played a key role in the team winning the national title in 2021 and 2022, and in the latter campaign he earned first-team All-American honors. Bowers took home the John Mackey award as the nation’s top tight end in each of t…

A few of the media on my blog in the #Caturday category...
Check them here https://www.didiermary.fr/category/cats-caturday/

Cats 4 Caturdays & more
Consulting, accompagnement & mentoring

This https://arxiv.org/abs/2305.06075 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

String Diagrams for Premonoidal Categories
Premonoidal categories are monoidal categories without the interchange law; effectful categories are premonoidal categories with a chosen monoidal subcategory of interchanging morphisms. In the same sense that string diagrams, pioneered by Joyal and Street, are an internal language for monoidal categories, we show that string diagrams with an added 'runtime wire', pioneered by Alan Jeffrey, are an internal language for effectful categories and can be used as string diagrams for effectful, premo…

This https://arxiv.org/abs/2403.10447 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Free Doubly-Infinitary Distributive Categories are Cartesian Closed
We delve into the concept of categories with products that distribute over coproducts, which we call doubly-infinitary distributive categories. We show various instances of doubly-infinitary distributive categories aiming for a comparative analysis with established notions such as extensivity, infinitary distributiveness, and cartesian closedness. Our exploration reveals that this condition represents a substantial extension beyond the classical understanding of infinitary distributive categori…