Tootfinder

This https://arxiv.org/abs/2310.05384 has been replaced.
link: https://scholar.google.com/scholar?q=a

Cartesian double theories: A double-categorical framework for categorical doctrines
The categorified theories known as "doctrines" specify a category equipped with extra structure, analogous to how ordinary theories specify a set with extra structure. We introduce a new framework for doctrines based on double category theory. A cartesian double theory is defined to be a small double category with finite products and a model of a cartesian double theory to be a finite product-preserving lax functor out of it. Many familiar categorical structures are models of cartesian double t…

GATlab: Modeling and Programming with Generalized Algebraic Theories
Owen Lynch, Kris Brown, James Fairbanks, Evan Patterson
https://arxiv.org/abs/2404.04837

GATlab: Modeling and Programming with Generalized Algebraic Theories
Categories and categorical structures are increasingly recognized as useful abstractions for modeling in science and engineering. To uniformly implement category-theoretic mathematical models in software, we introduce GATlab, a domain-specific language for algebraic specification embedded in a technical programming language. GATlab is based on generalized algebraic theories (GATs), a logical system extending algebraic theories with dependent types so as to encompass category theory. Using GATla…

This https://arxiv.org/abs/2401.13661 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Dévissage for generation in derived categories
This work exhibits that the essential image of the derived pushforward along a proper surjective morphism of Noetherian schemes generates the targets derived category of bounded complexes with coherent cohomology. There are two primary consequences to our work. First, we show that classical generators in the bounded derived category are preserved by derived pushforward along a proper surjective morphism of Noetherian schemes. Secondly, the bounded derived category coincides with the thick subca…

All We Know So Far
Great Australian Pods Podcast Directory: #GreatAusPods

All We Know So Far | Great Australian Pods Podcast Directory
Podcasts: All We Know So Far Host: Jonny Parkersen and Michael Parkersen Category: Kids & Family Sub-Category: Parenting & Pregnancy & Families First Episode: 2024 How we made our dream of becoming…

This https://arxiv.org/abs/2305.03120 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Free and co-free constructions for Hopf categories
We show that under mild conditions on the monoidal base category $\mathcal V$, the category ${\sf VHopf}$ of Hopf $\mathcal V$-categories is locally presentable and deduce the existence of free and cofree Hopf categories. We also provide an explicit description of the free and cofree Hopf categories over a semi-Hopf category. One of the conditions on the base category $\mathcal V$, states that endofunctors obtained by tensoring with a fixed object preserve jointly monic families, which leads us…