相关论文: Virtual concepts in the theory of accessible categ…
We discuss what it means for a symmetric monoidal category to be a module over a commutative semiring category. Each of the categories of (1) cartesian monoidal categories, (2) semiadditive categories, and (3) connective spectra can be…
In the paper "Extensional PERs" by P. Freyd, P. Mulry, G. Rosolini and D. Scott, a category $\mathcal{C}$ of "pointed complete extensional PERs" and computable maps is introduced to provide an instance of an \emph{algebraically compact…
We study the minimal dimension of the classifying space of the family of virtually cyclic subgroups of a discrete group. We give a complete answer for instance if the group is virtually poly-Z, word-hyperbolic or countable locally virtually…
In this paper, I will attempt to establish a framework for representation in virtual worlds that may allow for input data from many different scales and virtual physics to be merged. For example, a typical virtual environment must…
Category theory is a branch of mathematics that provides a formal framework for understanding the relationship between mathematical structures. To this end, a category not only incorporates the data of the desired objects, but also…
The aim of this paper is to study categorified algebraic structures and their pseudo- and lax homomorphisms using the framework of Lawvere $2$-theories, and more generally, (enhanced) $2$-dimensional sketches. The key notion we focus on is…
We establish {\em{virtual surjection to pairs}} (VSP) as a general criterion for the finite presentability of subdirect products of groups: if $\Gamma_1,...,\Gamma_n$ are finitely presented and $S<\Gamma_1\times...\times\Gamma_n$ projects…
We define a diagrammatic category that is equivalent to tilting representations for the orthogonal group. Our construction works in characteristic not equal to two. We also describe the semisimplification of this category.
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…
This paper proposes a change in perspective on the ``transformation of values'' problem: from ``searching for a single constant solution'' to ``characterizing the allocation space under objective constraints imposed by the physical…
We introduce a new notion of recursively generated enriched term which generalizes the one studied in joint work with Rosick\'y. These new terms come together with a notion of term-interpretability, which recovers the same type of…
The virtual reality (VR) provides us a three-dimensional, immersive, and fully interactive visualization environment. To make the best use of the VR's potential in scientific visualization, a VR visualization software named VFIVE has been…
In this article, the interplay between Vop\v{e}nka's principle, as well as its weaker counterpart, and presentable $\infty$-categories is studied. Analogous statements, arising after replacing categories with $\infty$-categories in the…
Let G be a finite group. The stable module category of G has been applied extensively in group representation theory. In particular, it has been used to great effect that it is a triangulated category which is compactly generated. Let H be…
We introduce a delooping model of relative exact categories. It gives us a condition that the negative K-group of a relative exact category becomes trivial.
We explain how recent developments in the fields of realisability models for linear logic -- or geometry of interaction -- and implicit computational complexity can lead to a new approach of implicit computational complexity. This…
We define relative support varieties with respect to some fixed module over a finite dimensional algebra. These varieties share many of the standard properties of classical support varieties. Moreover, when introducing finite generation…
We define and study the notion of a locally bounded enriched category over a (locally bounded) symmetric monoidal closed category, generalizing the locally bounded ordinary categories of Freyd and Kelly. In addition to proving several…
We introduce a new family of temporal logics designed to finely balance the trade-off between expressivity and complexity. Their key feature is the possibility of defining operators of a new kind that we call transformation operators. Some…
Special relativity, the symmetry breakdown in the electroweak standard model, and the dichotomy of the spacetime related transformations with the Lorentz group, on the one side, and the chargelike transformations with the hypercharge and…