Tootfinder

Projective and anomalous representations of categories and their linearizations
Domenico Fiorenza, Chetan Vuppulury
https://arxiv.org/abs/2506.01521 https:…

Projective and anomalous representations of categories and their linearizations
We invesigate the relation between projective and anomalous representations of categories, and show how to any anomaly $J\colon \mathcal{C}\to 2\mathrm{Vect}$ one can associate an extension $\mathcal{C}^J$ of $\mathcal{C}$ and a subcategory $\mathcal{C}^J_{\mathrm{ST}}$ of $\mathcal{C}^J$ with the property that: (i) anomalous representations of $\mathcal{C}$ with anomaly $J$ are equivalent to $\mathrm{Vect}$-linear functors $E\colon \mathcal{C}^J\to \mathrm{Vect}$, and (ii) these are in turn eq…

Ravens RB Keaton Mitchell: I feel like I'm better than before 2023 knee injury https://www.nfl.com/news/ravens-rb-keaton-mitchell-i-feel-like-i-m-better-than-before-2023-knee-injury

Suomalainen maitokulttuuri rakennettiin propagandan voimin https://animaliamedia.fi/suomalainen-maitokulttuuri-rakennettiin-propagandan-voimin/

Suomalainen maitokulttuuri rakennettiin propagandan voimin | Animalia-media
Vielä 1900-luvun alussa lehmänmaidolla oli arveluttava maine. Toisen eläimen maidon juonti ei ollut täysin itsestäänselvyys.

Bakersfield girl who faced deportation and loss of lifesaving medical care is allowed to stay in U.S. (Andrea Castillo/Los Angeles Times)
https://www.latimes.com/california/story/2025-06-03/bakersfield-girl-who-faced-deportation-loss-of-lifesaving-medical-care-granted-humanitarian-parole
http://www.memeorandum.com/250603/p134#a250603p134

😰 VR and AR simulations help users practice stress management in realistic scenarios
#vr

VR and AR simulations help users practice stress management in realistic scenarios
Everyday situations can sometimes feel like big stressors, whether it's delivering an important work presentation, attending a party full of strangers or confronting a partner. Talking to a friend or a therapist can help. But so can practice.

This https://arxiv.org/abs/2003.11202 has been replaced.
link: https://scholar.google.com/scholar?q=a

Set System Blowups
We prove that given a constant $k \ge 2$ and a large set system $\mathcal{F}$ of sets of size at most $w$, a typical $k$-tuple of sets $(S_1, \cdots, S_k)$ from $\mathcal{F}$ can be ``blown up" in the following sense: for each $1 \le i \le k$, we can find a large subfamily $\mathcal{F}_i$ containing $S_i$ so that for $i \neq j$, if $T_i \in \mathcal{F}_i$ and $T_j \in \mathcal{F}_j$ , then $T_i \cap T_j=S_i \cap S_j$. We also show that the answer to the multicolor version of the sunflower conje…

Medical device company Surmodics reports cyberattack, says it’s still recovering https://therecord.media/surmodics-medical-device-company-reports-cybersecurity-incident

This https://arxiv.org/abs/2501.17769 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Colimits of internal categories
We show that for an extensive $1$-category $\mathcal{E}$ with pullbacks and pullback stable coequalisers in which the forgetful functor $\mathcal{U}: \mathbf{Cat}(\mathcal{E})_1 \to \mathbf{Gph}(\mathcal{E})$ has left adjoint, the $2$-category $\mathbf{Cat}(\mathcal{E})$ of internal categories, functors and natural transformations has finite $2$-colimits. In addition, $\mathbf{Cat}(\mathcal{E})$ is extensive, has pullbacks and codescent coequalisers are stable under pullback along discrete Cond…

💪 Omnivorous? Vegan? Makes no difference to muscle building after weight training, study finds
https://medicalxpress.com/news/2025-04-omnivorous-vegan-difference-muscle-weight.html

Omnivorous? Vegan? Makes no difference to muscle building after weight training, study finds
A new study asked three questions about muscle protein synthesis in response to a nine-day diet and weight training regimen: First, does the source of protein—plant or animal-based—make any difference to muscle gain? Second, does it matter if total daily protein intake is evenly distributed throughout the day? And third, does a moderate but sufficient daily protein intake influence any of these variables? The answer to all three questions is "no," the researchers found.

This https://arxiv.org/abs/2407.01203 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

An elementary proof of a criterion for subfunctors of Ext to be closed
Let $\mathcal{A}$ be an abelian category and let $F$ be a subbifunctor of the additive bifunctor $\text{Ext}_{\mathcal{A}}^{1}(-,-)\colon \mathcal{A}^{\text{op}}\times \mathcal{A}\to \mathsf{Ab}$. Buan proved in [4] that $F$ is closed if, and only if, $F$ has the $3\times 3$-lemma property, a certain diagrammatic property satisfied by the class of $F$-exact sequences. The proof of this result relies on the theory of exact categories and on the Freyd--Mitchell embedding theorem, a very well-know…