相关论文: Virtual concepts in the theory of accessible categ…

We introduce a notion of partial presentability in parametrized higher category theory and investigate its interaction with the concepts of parametrized semiadditivity and stability from arXiv:2301.08240. In particular, we construct the…

A group is said to be self-similar provided it admits a faithful state-closed representation on some regular $m$-tree and the group is said to be transitive self-similar provided additionally it induces transitive action on the first level…

We show that elementary amenable groups, which have a bound on the orders of their finite subgroups, admit a finite dimensional model for the classifying space with virtually cyclic isotropy.

The visible orientation of human eyes creates some transparency about people's spatial attention and other mental states. This leads to a dual role of the eyes as a means of sensing and communication. Accordingly, artificial eye models are…

There exists a dispute in philosophy, going back at least to Leibniz, whether is it possible to view the world as a network of relations and relations between relations with the role of objects, between which these relations hold, entirely…

We introduce the class of projective reflection groups which includes all complex reflection groups. We show that several aspects involving the combinatorics and the representation theory of all non exceptional irreducible complex…

Given any map of finitely generated free modules, Buchsbaum and Eisenbud define a family of generalized Eagon-Northcott complexes associated to it. We give sufficient criterion for these complexes to be virtual resolutions, thus adding to…

Quantum gravity is extended to include purely virtual "cloud sectors", which allow us to define a complete set of point-dependent observables, including a gauge invariant metric and gauge invariant matter fields, and calculate their…

In the last years the debate on complexity has been developing and developing in transdisciplinary way to meet the need of explanation for highly organized collective behaviors and sophisticated hierarchical arrangements in physical,…

This note is intended to be a friendly introduction to virtual classes. We review virtual classes and we give a number of properties and applications. We also include a new virtual push-forward theorem and many computations of virtual…

We present a domain-specific type theory for constructions and proofs in category theory. The type theory axiomatizes notions of category, functor, profunctor and a generalized form of natural transformations. The type theory imposes an…

Relative realizability toposes satisfy a universal property that involves regular functors to other categories. We use this universal property to define what relative realizability categories are, when based on other categories than of the…

We introduce the notion of a $\textit{reflection fusion category}$, which is a type of a $G$-crossed category generated by objects of Frobenius-Perron dimension $1$ and $\sqrt{p}$, where $p$ is an odd prime. We show that such categories…

Morphisms between (formal) contexts are certain pairs of maps, one between objects and one between attributes of the contexts in question. We study several classes of such morphisms and the connections between them. Among other things, we…

We consider three (2-)categories and their (anti-)equivalence. They are the category of small abelian categories and exact functors, the category of definable additive categories and interpretation functors, the category of locally coherent…

Virtual constraints are relations imposed in a control system that become invariant via feedback, instead of real physical constraints acting on the system. Nonholonomic systems are mechanical systems with non-integrable constraints on the…

We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…

Visual representations are defined in terms of minimal sufficient statistics of visual data, for a class of tasks, that are also invariant to nuisance variability. Minimal sufficiency guarantees that we can store a representation in lieu of…

Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous…

In this paper, we try to answer the following question: given a modular tensor category $\A$ with an action of a compact group $G$, is it possible to describe in a suitable sense the ``quotient'' category $\A/G$? We give a full answer in…