Related papers: Locally Cartesian Closed Categories
A non-self-contained gathering of notes on category theory, including the definition of locally cartesian closed category, of the cartesian structure in slice categories, or of the pseudo-cartesian structure on Eilenberg-Moore categories.…
A notion of a coring extension is defined and it is related to the existence of an additive functor between comodule categories that factorises through forgetful functors. This correspondence between coring extensions and factorisable…
We investigate categories in which products distribute over coproducts, a structure we call doubly-infinitary distributive categories. Through a range of examples, we explore how this notion relates to established concepts such as…
In this note, we show that the category of strongly central series admits co-induced actions, which means that it is Locally Algebraically Cartesian Closed. We also show that some co-induction functors exist in the category of topological…
A notion of support for objects in any Grothendieck category is introduced. This is based on the spectral category of a Grothendieck category and uses its Boolean lattice of localising subcategories. The support provides a classification of…
The notion of Kan extendable subcategories was initially introduced to define the category of compactly generated fibrewise topological spaces over a T1 base space and to establish its cartesian closure. In this paper, we show that the same…
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…
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,…
The aim of this paper is to introduce the notion of $a$-locally closed set by utilizing $a$-open sets defined by Ekici and to study some properties of this new notion. Also, some characterizations and many fundamental results regarding this…
We show that a version of Martin-L\"of type theory with an extensional identity type former I, a unit type N1 , Sigma-types, Pi-types, and a base type is a free category with families (supporting these type formers) both in a 1- and a…
This is a conspectus of definite integrals, products and series. These formulae involve special functions in the integrand and summand functions and closed form solutions. Some of the special cases are stated in terms of fundamental…
We prove that the category of c-spaces with continuous maps is not cartesian closed. As a corollary the category of locally finitary compact spaces with continuous maps is also not cartesian closed.
Based on Gandy's principles for models of computation we give category-theoretic axioms describing locally deterministic updates to finite objects. Rather than fixing a particular category of states, we describe what properties such a…
We study the transfer of (co)silting objects in derived categories of module categories via the extension functors induced by a morphism of commutative rings. It is proved that the extension functors preserve (co)silting objects of…
Categories are coreflectively embedded in multicategories via the "discrete cocone" construction, the right adjoint being given by the monoid construction. Furthermore, the adjunction lifts to the "cartesian level": preadditive categories…
We give an elementary characterization of those quantaloids Q for which the category Cat(Q) of Q-enriched categories and functors is cartesian closed. We then unify several known cases (previously proven using ad hoc methods) and we give…
If a compact closed category has finite products or finite coproducts then it in fact has finite biproducts, and so is semi-additive.
In this thesis we define the notion of a locally stratified space. Locally stratified spaces are particular kinds of streams and d-spaces which are locally modelled on stratified spaces. We construct a locally presentable and cartesian…
Categorical bundles provide a natural framework for gauge theories involving multiple gauge groups. Unlike the case of traditional bundles there are distinct notions of triviality, and hence also of local triviality, for categorical…
This paper establishes a purely syntactic representation for the category of algebraic L-domains with Scott-continuous functions as morphisms. The central tool used here is the notion of logical states, which builds a bridge between…