Related papers: Consciousness in a Higher Categorical Context
Machine learning algorithms have achieved superhuman performance in specific complex domains. However, learning online from few examples and compositional learning for efficient generalization across domains remain elusive. In humans, such…
We consider the 3-category $2\mathfrak{C}at$ whose objects are 2-categories, 1-morphisms are lax functors, 2-morphisms are lax transformations and 3-morphisms are modifications. The aim is to show that it carries interesting…
We extend the classical notion of a Reedy category so as to allow non-trivial automorphisms. Our extension includes many important examples occuring in topology such as Segal's category Gamma, or the total category of a crossed simplicial…
In this paper, we establish a dual framework for Neeman's results concerning triangulated categories with compact silting objects by employing Brown--Comenetz duality. This framework introduces an intrinsic non-compact subcategory, provides…
We extend the notion of rational points and cohomological obstructions on varieties to categories fibred in groupoids. We also establish the generalized theory of descent by torsors. Then we interpret the obstruction given by the second…
Understanding why a classification model prefers one class over another for an input instance is the challenge of contrastive explanation. This work implements concept-based contrastive explanations for image classification by leveraging…
In this paper, we first study hypergraph rewriting in categorical terms in an attempt to define the notion of events and develop foundations of causality in graph rewriting. We introduce novel concepts within the framework of double-pushout…
We show the equivalence of two kinds of strict multiple category, namely the well known globular omega-categories, and the cubical omega-categories with connections.
We prove that the set of concordance classes of sections of an infinity-sheaf on a manifold is representable, extending a theorem of Madsen and Weiss. This is reminiscent of an h-principle in which the role of isotopy is played by…
We propose the quantum mechanical description of complex systems should be performed using two types of causality relation: the ordering relation ($x\prec y$) and the subset relation ($A\subseteq B$). The structures with two ordering…
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…
We develop a notion of causal order on a generic manifold as independent of the underlying differential and topological structure. We show that sufficiently regular causal orders can be recovered from a distinguished algebra of sets, which…
A new prior is proposed for learning representations of high-level concepts of the kind we manipulate with language. This prior can be combined with other priors in order to help disentangling abstract factors from each other. It is…
In this article we review how categorical equivalences are realized by renormalization group flow in physical realizations of stacks, derived categories, and derived schemes. We begin by reviewing the physical realization of sigma models on…
Consciousness is the process by which one attributes `meaning' to the world. Considering F$\phi$llesdal's definition of `meaning' as the joint product of all `evidence' that is available to those who `communicate', we conclude that science…
For a Coxeter system and a representation $V$ of this Coxeter system, Soergel defined a category which is now called the category of Soergel bimodules and proved that this gives a categorification of the Hecke algebra when $V$ is reflection…
The notion of pseudocategory, as considered in [11], is extended from the context of a 2-category to the more general one of a sesquicategory, which is considered as a category equipped with a 2-cell structure. Some particular examples of…
In this thesis, we develop the theory of bifibrations of polycategories. We start by studying how to express certain categorical structures as universal properties by generalising the shape of morphism. We call this phenomenon…
This paper deals with classifying ambiguities for Multimodal Languages. It evolves the classifications and the methods of the literature on ambiguities for Natural Language and Visual Language, empirically defining an original…
We define a 2-category structure (Pre-Orb) on the category of reduced complex orbifold atlases. We construct a 2-functor F from (Pre-Orb) to the 2-category (Grp) of proper \'etale effective groupoid objects over the complex manifolds. Both…