Tootfinder

This https://arxiv.org/abs/2111.14796 has been replaced.
link: https://scholar.google.com/scholar?q=a

Familial Monads as Higher Category Theories
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any higher category structure which arises as algebras for a familially representable monad on a presheaf category, then use this to describe several examples relating to higher category theory and cubical sets. The proof of this characterization avoids tedious natur…

This https://arxiv.org/abs/2505.22171 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

2-Category of Topological Quantum Computation
Unitary Ribbon Fusion Categories (URFC) formalize anyonic theories. It has been widely assumed that the same category formalizes a topological quantum computing model. However, in previous work, we addressed and resolved this confusion and demonstrated while the former could be any fusion category, the latter is always a subcategory of Hilb. In this paper, we argue that a categorical formalism that captures and unifies both anyonic theories (the Hardware of quantum computing) and a model of top…

On the IKEA SMAKLIG Built-in Induction Hob: Review - Is an induction hob better than cooking with gas? How about health and carbon? #induction #cutCarbon #airQuality -

On the IKEA SMAKLIG Built-in Induction Hob: Review
Is an induction hob better than cooking with gas? How about health and carbon? #induction #cutCarbon #airQuality

This https://arxiv.org/abs/1712.00555 has been replaced.
link: https://scholar.google.com/scholar?q=a

A monadicity theorem for higher algebraic structures
We develop a theory of Eilenberg-Moore objects in any $(\infty,2)$-category and extend Barr-Beck's monadicity theorem to any $(\infty,2)$-category that admits Eilenberg-Moore objects. We apply this result to various $(\infty,2)$-categories of higher algebraic structures to obtain a monadicity theorem for enriched $\infty$-categories, $\infty$-operads and higher Segal objects. Analyzing Eilenberg-Moore objects in the $(\infty,2)$-categories of symmetric monoidal $\infty$-categories and lax (opla…

arxiv_citation: arXiv citation networks (1993-2003)
Citations among papers posted on arxiv.org under the hep-ph and hep-th categories, between 1993 and 2003. This time begins a few months after axiv was launched. If a paper i cites a paper j also in this data set, then a directed edge connects i to j. (Papers not in the data set are excluded.) These data were originally released as part of the 2003 KDD Cup.
This network has 34546 nodes and 421578 edges.
Tags: Informational,…

This https://arxiv.org/abs/2406.13240 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

$ω$-weak equivalences between weak $ω$-categories
We study $ω$-weak equivalences between weak $ω$-categories in the sense of Batanin-Leinster. Our $ω$-weak equivalences are strict $ω$-functors satisfying essential surjectivity in every dimension, and when restricted to those between strict $ω$-categories, they coincide with the weak equivalences in the model category of strict $ω$-categories defined by Lafont, Métayer, and Worytkiewicz. We show that the class of $ω$-weak equivalences has the 2-out-of-3 property. We also consider a gene…

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…

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…

This https://arxiv.org/abs/2503.17319 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The algebraic internal groupoid model of Martin-Löf type theory
We extend the model structure on the category $\mathbf{Cat}(\mathcal{E})$ of internal categories studied by Everaert, Kieboom and Van der Linden to an algebraic model structure. Moreover, we show that it restricts to the category of internal groupoids. We show that in this case, the algebraic weak factorisation system that consists of the algebraic trivial cofibrations and algebraic fibrations forms a model of Martin-Löf type theory. Taking $\mathcal{E} = \mathbf{Set}$ and forgetting the algeb…

This https://arxiv.org/abs/2001.09029 has been replaced.
link: https://scholar.google.com/scholar?q=a

Rewriting Structured Cospans
To support the study of compositional networks, we further develop the formalism of structured cospans. To enable rewriting, we introduce a category whose objects are structured cospans and characterize conditions under which this category is a topos or is adhesive. We then define a structured cospan grammar and language, using a 2-category framework. As an application, we demonstrate that for various sorts of graphs, hypergraphs, and Petri nets, any grammar induces the same language as its cor…