Related papers: Category theory for scientists (Old version)
We give a presentation of Feynman categories from a representation--theoretical viewpoint. Feynman categories are a special type of monoidal categories and their representations are monoidal functors. They can be viewed as a far reaching…
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,…
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from areas as diverse as topology, quantum algebra, mathematical physics,…
This paper presents a batch classifier that has been improved from the earlier version and fixed a mistake in the earlier paper. Two important changes have been made. Each category is represented by a classifier, where each classifier…
We propose a categorical framework to reason about scientific explanations: descriptions of a phenomenon meant to translate it into simpler terms, or into a context that has been already understood. Our motivating examples come from systems…
Actions of monoidal categories on categories, also known as actegories, have been familiar to category theorists for a long time, and yet a comprehensive overview of this topic seems to be missing from the literature. Recently, actegories…
This paper proposes a formal cognitive framework for problem solving based on category theory. We introduce cognitive categories, which are categories with exactly one morphism between any two objects. Objects in these categories are…
We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…
Category theory provides a means through which many far-ranging fields of mathematics can be related by their similar structure. In a paper by Robinson [2], this interconnectivity afforded by categorical perspectives allowed for the…
A concept of "evolving categories" is suggested to build a simple, scalable, mathematically consistent framework for representing in uniform way both data and algorithms. A state machine for executing algorithms becomes clear, rich and…
We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded…
An outline and summary of four new potential applications of category theory to OOP research are presented. These include (1) the use of operads to model Java subtyping, (2) the use of Yoneda's lemma and representable functors in the…
We give a self-contained introduction to accessible categories and how they shed light on both model- and set-theoretic questions. We survey for example recent developments on the study of presentability ranks, a notion of cardinality…
We discuss the role of propositions, truth, context and observers in scientific theories. We introduce the concept of generalized proposition and use it to define an algorithm for the classification of any scientific theory. The algorithm…
In this Chapter, I will explore the use of modeling in order to understand how Science works. I will discuss the modeling of scientific communities, providing a general, non-comprehensive overview of existing models, with a focus on the use…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
We apply category theory to extract multimodal document structure which leads us to develop information theoretic measures, content summarization and extension, and self-supervised improvement of large pretrained models. We first develop a…
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…
This is a report on aspects of the theory and use of monoidal categories. The first section introduces the main concepts through the example of the category of vector spaces. String notation is explained and shown to lead naturally to a…
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…