Related papers: Towards a double operadic theory of systems
Categories, n-categories, double categories, and multicategories (among others) all have similar definitions as collections of cells with composition operations. We give an explicit description of the information required to define any…
We propose a new unified framework for Thompson-like groups using a well-known device called operads and category theory as language. We discuss examples of operad groups which have appeared in the literature before. As a first application,…
Expansion of the categorical point of view on many areas of the mathematics and mathematical physics will cause to deeper understanding of genuine features of these problems. New applications of categorical methods are connected with new…
The development of mathematics has been characterized by the increasing interconnectivity of seemingly separate disciplines. Such interplay has been facilitated by a massive development in formalism; category theory has provided a common…
It came to the attention of myself and the coauthors of (S., Rozowski, Silva, Rot, 2022) that a number of process calculi can be obtained by algebraically presenting the branching structure of the transition systems they specify. Labelled…
There are many books designed to introduce category theory to either a mathematical audience or a computer science audience. In this book, our audience is the broader scientific community. We attempt to show that category theory can be…
We introduce the classical theory of the interplay between group theory and topology into the context of operads and explore some applications to homotopy theory. We first propose a notion of a group operad and then develop a theory of…
We establish model category structures on algebras and modules over operads in symmetric spectra, and study when a morphism of operads induces a Quillen equivalence between corresponding categories of algebras (resp. modules) over operads.
This work presents a detailed analysis of the combinatorics of modular operads. These are operad-like structures that admit a contraction operation as well as an operadic multiplication. Their combinatorics are governed by graphs that admit…
This paper initiates the dialectical approach to net theory. This approach views nets as special, but very important and natural, dialectical systems. By following this approach, a suitably generalized version of nets, called dialectical…
Associative rings A, B are called Morita equivalent when the categories of left modules over them are equivalent. We call two classical linear operads P, Q Morita equivalent if the categories of algebras over them are equivalent. We…
The primary contribution of this paper is to give a formal, categorical treatment to Penrose's abstract tensor notation, in the context of traced symmetric monoidal categories. To do so, we introduce a typed, sum-free version of an abstract…
We give sufficient conditions for the existence of a model structure on operads in an arbitrary symmetric monoidal model category. General invariance properties for homotopy algebras over operads are deduced.
When designing plans in engineering, it is often necessary to consider attributes associated to objects, e.g. the location of a robot. Our aim in this paper is to incorporate attributes into existing categorical formalisms for planning,…
This paper introduces the concept of distorted monoidal categories, a generalization of monoidal and braided monoidal categories that supports non-reversible and direction-sensitive tensor structures. Unlike the classical setting, where the…
Network models, which abstractly are given by lax symmetric monoidal functors, are used to construct operads for modeling and designing complex networks. Many common types of networks can be modeled with simple graphs with edges weighted by…
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
We consider a class of block operator matrices arising in the study of scattering passive systems, especially in the context of boundary control problems. We prove that these block operator matrices are indeed a subclass of block operator…
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…
Complex systems of systems (SoS) are characterized by multiple interconnected subsystems. Typically, each subsystem is designed and analyzed using methodologies and formalisms that are specific to the particular subsystem model of…