Related papers: Double categories of relations relative to factori…
We define a 2-category structure (Pre-Orb) on the category of reduced complex orbifold atlases. We construct a 2-functor F from (Pre-Orb) to the 2-category (Grp) of proper \'etale effective groupoid objects over the complex manifolds. Both…
We define the twisted tensor product of two enriched categories, which generalizes various sorts of `products' of algebraic structures, including the bicrossed product of groups, the twisted tensor product of (co)algebras and the double…
Given a formal context, an ordinal factor is a subset of its incidence relation that forms a chain in the concept lattice, i.e., a part of the dataset that corresponds to a linear order. To visualize the data in a formal context, Ganter and…
In this paper we use the equivariant version of factorization homology constructed using the parametrized higher category theory and show that it can be used to describe the results used in the series of papers.
Factor analysis provides linear factors that describe relationships between individual variables of a data set. We extend this classical formulation into linear factors that describe relationships between groups of variables, where each…
This document is centered around a main idea: simplicial categories, by which we mean simplicial objects in the category of categories, can be treated as a two-fold categorical structure and their double category theory is homotopically…
Originally enriched categories were defined over a monoidal category, but it was gradually realized that important examples can only be included when one enriches over more general structures such as bicategories and virtual double…
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…
A certain amount of category theory is developed in an arbitrary finitely complete category with a factorization system on it, playing the role of the comprehensive factorization system on Cat. Those aspects related to the concepts of…
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…
Regular logic is the fragment of first order logic generated by $=$, $\top$, $\wedge$, and $\exists$. A key feature of this logic is that it is the minimal fragment required to express composition of binary relations; another is that it is…
In this work we discuss a new type of factorisation systems for \textbf{Ord}-enriched categories. We start by defining the new notion of lax weak orthogonality, which involves the existence of lax diagonal morphisms for lax squares. Using…
Algebraic theories with dependency between sorts form the structural core of Martin-L\"of type theory and similar systems. Their denotational semantics are typically studied using categorical techniques; many different categorical…
Factorizations over cones and their duals play central roles for many areas of mathematics and computer science. One of the reasons behind this is the ability to find a representation for various objects using a well-structured family of…
This paper develops a systematic framework for integrating local categories that model logical connectives using higher category theory. By extending these local categories into a unified two-category enriched with natural isomorphisms, the…
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…
Recent work in set theory indicates that there are many different notions of 'set', each captured by a different collection of axioms, as proposed by J. Hamkins in [Ham11]. In this paper we strive to give one class theory that allows for a…
Two doubly indexed families of polynomials in several indeterminates are considered. They are related to the falling and rising factorials in a similar way as the potential polynomials (introduced by L. Comtet) are related to the ordinary…
In this paper we develope a categorical theory of relations and use this formulation to define the notion of quantization for relations. Categories of relations are defined in the context of symmetric monoidal categories. They are shown to…
We show how Stone duality can be extended from maps to relations. This is achieved by working order enriched and defining a relation from A to B as both an order-preserving function from the opposite of A times B to the 2-element chain and…