Related papers: Equ-saturating categories
Categorical compositional distributional semantics is a model of natural language; it combines the statistical vector space models of words with the compositional models of grammar. We formalise in this model the generalised quantifier…
We prove existence of equalizers in certain categories of cocomplete cocategories. This allows us to complete the proof of the fact that A-infinity functor categories arise as internal Hom-objects in the category of differential graded…
Category theory unifies mathematical concepts, aiding comparisons across structures by incorporating objects and morphisms, which capture their interactions. It has influenced areas of computer science such as automata theory, functional…
We study centrality of morphisms in a setting derived from that of a pointed category in which binary products commute with coequalisers. The main results of this paper show that much of the behaviour of central morphisms for unital…
EI-categories are a simultaneous generalisation of finite groups and finite quivers without oriented cycles. It is therefore a natural question to ask for a characterisation of finite representation type. For special classes of…
In the context of protomodular categories, several additional conditions have been considered in order to obtain a closer group-like behavior. Among them are locally algebraic cartesian closedness and algebraic coherence. The recent notion…
We introduce relative homological and weakly homological categories, where ``relative'' refers to a distinguished class of normal epimorphisms. It is a generalization of homological categories, but also protomodular categories can be…
Let k be a commutative ring with unit. We endow the categories of filtered complexes and of bicomplexes of k-modules, with cofibrantly generated model structures, where the class of weak equivalences is given by those morphisms inducing a…
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…
We introduce the notion of a logical model category which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it.…
We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension…
We define notions of generically and coarsely computable relations and structures and functions between structures. We investigate the existence and uniqueness of equivalence structures in the context of these definitions
This thesis deals with two main topics: virtual double categories as semantics environments for predicate logic, and a syntactic presentation of virtual double categories as a type theory. One significant principle of categorical logic is…
Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.
We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the…
Presentations of categories are a well-known algebraic tool to provide descriptions of categories by means of generators, for objects and morphisms, and relations on morphisms. We generalize here this notion, in order to consider situations…
We introduce a notion of a filtered model structure and use this notion to produce various model structures on pro-categories. This framework generalizes several known examples. We give several examples, including a homotopy theory for…
We study the central objects of symbolic dynamics, that is, subshifts and block maps, from the perspective of basic category theory, and present several natural categories with subshifts as objects and block maps as morphisms. Our main…
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…
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…