Related papers: Relevant Categories and Partial Functions

Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…

It is known that monoidal categories have a finite definition, whereas multicategories have an infinite (albeit finitary) definition. Since monoidal categories correspond to representable multicategories, it goes without saying that…

We describe all left continuous triangular norms for which the category [0,1]-Cat of real-enriched categories and functors is cartesian closed. We furthermore show that the cartesian closedness of [0,1]-Cat is equivalent to the cartesian…

Relational structures are emerging as ubiquitous mathematical machinery in the semantics of open systems of various kinds. Cartesian bicategories are a well-known categorical algebra of relations that has proved especially useful in recent…

We introduce, for every positive integer n, the notion of an n-relative category and show that the category of the small n-relative categories is a model for the homotopy theory of n-fold homotopy theories, i.e. homotopy theories of ... of…

It is well-known that reduced smooth orbifolds and proper effective foliation Lie groupoids form equivalent categories. However, for certain recent lines of research, equivalence of categories is not sufficient. We propose a notion of maps…

Let $[0,1]_*$ be the unit interval $[0,1]$ equipped with a continuous t-norm $*$. It is shown that the category of $[0,1]_*$-sets is cartesian closed if, and only if, $*$ is the minimum t-norm on $[0,1]$.

Let $\&$ be a continuous triangular norm on the unit interval $[0,1]$ and $\mathbf{A}$ be a cartesian closed and stable subconstruct of the category consisting of all real-enriched categories. Firstly, it is shown that the category…

Category theory has foundational importance because it provides conceptual lenses to characterize what is important in mathematics. Originally the main lenses were universal mapping properties and natural transformations. In recent decades,…

We prove that various classical conformal diffeomorphism groups, which are known to be essential [1], are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of a cohomological…

We define an interesting sub-category of the category of simplicial sets, $\Sr$, whose objects are called regular. Both it and the subcategory ${\cal S}_{f-{\rm reg}}$ of finite regular simplicial sets have good stability properties under…

In this chapter we survey some particular topics in category theory in a somewhat unconventional manner. Our main focus will be on monoidal categories, mostly symmetric ones, for which we propose a physical interpretation. These are…

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…

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…

A groupoid is a small category in which all morphisms are isomorphisms. An inductive groupoid is a specialised groupoid whose object set is a regular biordered set and the morphisms admit a partial order. A normal category is a specialised…

We introduce the notion of residual finiteness for categories. In analogy with the group-theoretic setting, we prove that free categories and finitely generated subcategories of finite-dimensional vector spaces are residually finite.…

We study the monoidal closed category of symmetric multicategories, especially in relation with its cartesian structure and with sequential multicategories (whose arrows are sequences of concurrent arrows in a given category). Then we…

Categorical structures and their pseudomaps rarely form locally presentable 2-categories in the sense of Cat-enriched category theory. However, we show that if the categorical structure in question is sufficiently weak (such as the…

We introduce a new form of logical relation which, in the spirit of metric relations, allows us to assign each pair of programs a quantity measuring their distance, rather than a boolean value standing for their being equivalent. The…

We prove a categorical duality between a class of abstract algebras of partial functions and a class of (small) topological categories. The algebras are the isomorphs of collections of partial functions closed under the operations of…