Related papers: Symmetric Monoidal Categories with Attributes

We study properties of the cubical Joyal model structures on cubical sets by means of a combinatorial construction which allows for convenient comparisons between categories of cubical sets with and without symmetries. In particular, we…

This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding…

I describe a generalization of the notion of operadic category due to Batanin and Markl. For each such operadic category I describe a skew monoidal category of collections, such that a monoid in this skew monoidal category is precisely an…

Identifying and categorizing specific robot tasks, behaviors, and resources is an essential precursor to reproducing and evaluating robotics experiments across laboratories and platforms. Without some means of capturing how one environment,…

Recently, the theory of symmetric spaces has come to play an increased role in the physics of integrable systems and in quantum transport problems. In addition, it provides a classification of random matrix theories. In this paper we give a…

We introduce semidirect products of skew monoidal categories as a categorification of semidirect products of monoids (or, perhaps more familiarly, of groups). We also discuss how this construction interacts with monoidal, autonomous and…

Over the past two decades machine learning has permeated almost every realm of technology. At the same time, many researchers have begun using category theory as a unifying language, facilitating communication between different scientific…

The basic data for a skew-monoidal category are the same as for a monoidal category, except that the constraint morphisms are no longer required to be invertible. The constraints are given a specific orientation and satisfy Mac Lane's five…

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…

The centre of a monoidal category is a braided monoidal category. Monoidal categories are monoidal objects (or pseudomonoids) in the monoidal bicategory of categories. This paper provides a universal construction in a braided monoidal…

The term robot generally refers to a machine that looks and works in a way similar to a human. The modern industry is rapidly shifting from manual control of systems to automation, in order to increase productivity and to deliver quality…

An object $P$ in a monoidal category $\mathcal{C}$ is called pivotal if its left dual and right dual objects are isomorphic. Given such an object and a choice of dual $Q$, we construct the category $\mathcal{C}(P,Q)$, of objects which…

We explain the sense in which a warping on a monoidal category is the same as a pseudomonad on the corresponding one-object bicategory, and we describe extensions of this to the setting of skew monoidal categories: these are a…

This note remarks that the correspondence between non-unital algebras and augmented unital algebras can be derived from Hovey's Smith ideal theory. Applying Smith ideal theory of stable symmetric monoidal model category, we formulate…

We build a model structure from the simple point of departure of a structured interval in a monoidal category - more generally, a structured cylinder and a structured co-cylinder in a category.

Human-centered environments are rich with a wide variety of spatial relations between everyday objects. For autonomous robots to operate effectively in such environments, they should be able to reason about these relations and generalize…

Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…

We use categorification of monoid actions to study algebraic geometry over symmetric monoidal categories. This brings together the relative algebraic geometry over symmetric monoidal categories developed by To\"{e}n and Vaqui\'{e}, along…

We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…

The aim of this article is to study certain categorical-algebraic frameworks for basic homological algebra, introduced in arXiv:2404.15896, with the aim of better understanding the differences between them. We focus on homological…