Related papers: Categories of categories
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
Written to be contributed as the "mathematical modeling" chapter of a book, edited by Elaine Landry, to be titled "Categories for the Working Philosopher". In this chapter, category theory is presented as a mathematical modeling framework…
Internal categories feature notions of limit and completeness, as originally proposed in the context of the effective topos. This paper sets out the theory of internal completeness in a general context, spelling out the details of the…
This paper provides a comprehensive overview of some of the foundational properties of categories enriched over quantaloids, along with several new results. We demonstrate that the category whose objects are quantaloid-enriched categories…
In context of efforts of composing category-theoretic and logical methods in the area of knowledge representation we propose the notion of conceptory. We consider intersection/union and other constructions in conceptories as expressive…
We consider and characterize classes of finite and countably categorical structures and their theories preserved under $E$-operators and $P$-operators. We describe $e$-spectra and families of finite cardinalities for structures belonging to…
Compact categories have lately seen renewed interest via applications to quantum physics. Being essentially finite-dimensional, they cannot accomodate (co)limit-based constructions. For example, they cannot capture protocols such as quantum…
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 attempt is to give a formal concpet of system, and with this provide a definition of category, that will also satisfy the definition of a system. An axiomatic base is given, for constructing the group of integers. In the process, we…
Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete…
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 establish a correspondence between consistent comprehension schemes and complete orthogonal factorisation systems. The comprehensive factorisation of a functor between small categories arises in this way. Similar factorisation systems…
In this note we characterize, within the framework of the theory of finite set, those categories of graphs that are {\em algebraic universal} in the sense that every concrete category embeds in them. The proof of the characterization is…
The Euler characteristic of a finite category is defined and shown to be compatible with Euler characteristics of other types of object, including orbifolds. A formula for the cardinality of the colimit of a diagram of sets is proved,…
We examine various categorical structures that can and cannot be constructed. We show that total computable functions can be mimicked by constructible functors. More generally, whatever can be done by a Turing machine can be constructed by…
Certain results involving "higher structures" are not currently accessible to computer formalization because the prerequisite $\infty$-category theory has not been formalized. To support future work on formalizing $\infty$-category theory…
We present a new, category theoretic point of view on finite Ramsey theory. Our aims are as follows: -- to define the category theoretic notions needed for the development of finite Ramsey Theory, -- to state, in terms of these notions, the…
An algebraic formalism for the study of interacting particle systems is developed. Particle processes are described in terms of the category theory. The problem for the unique description of these processes is discussed. Categories relevant…
Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility…
Lenses are an important tool in applied category theory. While individual lenses have been widely used in applications, many of the mathematical properties of the corresponding categories of lenses have remained unknown. In this paper, we…