Related papers: A Model of Parametric Dependent Type Theory in Bri…
We study the relationship between presheaf constructions and free cocompletions in the context of formal category theory, elucidating the coincidence between the two concepts in familiar settings. We show that, in a virtual equipment…
Building on work of Marta Bunge in the one-categorical case, we characterize when a given model category is Quillen equivalent to a presheaf category with the projective model structure. This involves introducing a notion of homotopy atoms,…
Inferring the potential consequences of an unobserved event is a fundamental scientific question. To this end, Pearl's celebrated do-calculus provides a set of inference rules to derive an interventional probability from an observational…
Bayesian networks are a widely-used class of probabilistic graphical models capable of representing symmetric conditional independence between variables of interest using the topology of the underlying graph. For categorical variables, they…
We study the dependent type theory CaTT, introduced by Finster and Mimram, which presents the theory of weak $\omega$-categories, following the idea that type theories can be considered as presentations of generalized algebraic theories.…
In the authors book, Associative Algebraic Geometry, 2023, and the following article Shemes of Associative Algebras,\\ https://doi.org/10.48550/arXiv.2410.17703,2024, we use an algebraization of the semi-local formal moduli of simple…
In many supervised learning tasks, the entities to be labeled are related to each other in complex ways and their labels are not independent. For example, in hypertext classification, the labels of linked pages are highly correlated. A…
Most traditional models of uncertainty have focused on the associational relationship among variables as captured by conditional dependence. In order to successfully manage intelligent systems for decision making, however, we must be able…
We propose a semantic foundation for logics for reasoning in settings that possess a distinction between equality of variables, a coarser equivalence of variables, and a notion of conditional independence between variables. We show that…
This paper introduces an expressive class of indexed quotient-inductive types, called QWI types, within the framework of constructive type theory. They are initial algebras for indexed families of equational theories with possibly…
In this paper, which is subsequent to our previous paper [PS] (but can be read independently from it), we continue our study of the closed model structure on the category $\mathrm{Cat}_{\mathrm{dgwu}}(\Bbbk)$ of small weakly unital dg…
Classical design theory treats the type of an object as a given: the designer decides in advance that this will be a cup, then optimizes its parameters. This paper argues that object type is not a presupposition but an inference, something…
Here, we present a subcategory pEff of Hyland's Effective Topos Eff which can be considered a predicative variant of Eff itself. The construction of pEff is motivated by the desire of providing a "predicative" categorical universe of…
Human brain structural networks contain sets of centrally embedded hub regions that enable efficient information communication. However, it remains largely unknown about categories of structural brain hubs and their microstructural,…
We introduce structural causal bottleneck models (SCBMs), a novel class of structural causal models. At the core of SCBMs lies the assumption that causal effects between high-dimensional variables only depend on low-dimensional summary…
We develop a general theory of extensions of flat functors along geometric morphisms of toposes, and apply it to the study of the class of theories whose classifying topos is equivalent to a presheaf topos. As a result, we obtain a…
For any connected and simply connected parasymplectic space $(\mathrm{X},\omega)$ with group of periods $\mathrm{P}_\omega \subsetneq \mathbf{R}$, we construct a prequantum groupoid $\pmb{\mathrm{T}}_\omega$ as a diffeological quotient of…
We construct a co-$t$-structure on the derived category of coherent sheaves on the nilpotent cone $\mathcal{N}$ of a reductive group, as well as on the derived category of coherent sheaves on any parabolic Springer resolution. These…
Dependency networks (Heckerman et al., 2000) provide a flexible framework for modeling complex systems with many variables by combining independently learned local conditional distributions through pseudo-Gibbs sampling. Despite their…
In this paper we continue the study of the most important structures on C-systems, the structures that correspond, in the case of the syntactic C-systems, to the $(Pi,lambda,app,beta,eta)$-system of inference rules. One such structure was…