Related papers: Archimedean Type Conditions in Categories
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…
Modelling concept representation is a foundational problem in the study of cognition and linguistics. This work builds on the confluence of conceptual tools from G\"ardenfors semantic spaces, categorical compositional linguistics, and…
The study of categories that abstract the structural properties of relations has been extensively developed over the years, resulting in a rich and diverse body of work. This paper strives to provide a modern presentation of these…
On objects of a triangulated category with a stability condition, we construct a topology.
For an exact category we provide two constructions of an ambient category in which the initial category is resolving: In the derived category and in the Gabriel--Quillen embedding. For the first construction we describe a pre-aisle and its…
We consider the problem where a set of individuals has to classify $m$ objects into $p$ categories by aggregating the individual classifications, and no category can be left empty. An aggregator satisfies \emph{Expertise} if individuals are…
This is a companion overview paper to arXiv:2409.17489: we give all the main definitions, constructions and statements, but no proofs.
We discuss the notion of strongly unbounded type for abelian length categories; this is closely related to the Second Brauer-Thrall Conjecture for artin algebras. A new ingredient is the space of characters in the sense of Crawley-Boevey.
A new construction to associate an internal category to an enriched one is presented. The key concept is that of extensive ambient category, and the construction follows the one that associates a category whose idempotents split to a given…
Bicategories of spans are characterized as cartesian bicategories in which every comonad has an Eilenberg-Moore ob ject and every left adjoint arrow is comonadic.
This paper introduces categories of assemblies which are closely connected to realizability interpretations and which are based on an important subcategory of the effective topos. There is a list of properties which characterize these…
We call a triangulated category \emph{hereditary} provided that it is equivalent to the bounded derived category of a hereditary abelian category, where the equivalence is required to commute with the translation functors. If the…
We show how the notion of intercategory encompasses a wide variety of three-dimensional structures from the literature, notably duoidal categories, monoidal double categories, cubical bicategories, double bicategories and Gray categories.…
Epistemic uncertainty arises in lack of complete knowledge about the state of a system. There are multiple mathematical frameworks for measuring such uncertainty quantitatively, often referred to as imprecise probability theories. Inspired…
The purpose of this paper is to show that the dual notions of elements & distinctions are the basic analytical concepts needed to unpack and analyze morphisms, duality, and universal constructions in the Sets, the category of sets and…
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.…
We show that if A is an abelian category satisfying certain mild conditions, then one can introduce the concept of a moduli space of (semi)stable objects which has the structure of a projective algebraic variety. This idea is applied to…
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 propose an abstract notion of a type theory to unify the semantics of various type theories including Martin-L\"{o}f type theory, two-level type theory and cubical type theory. We establish basic results in the semantics of type theory:…
We introduce judgemental theories and their calculi as a general framework to present and study deductive systems. As an exemplification of their expressivity, we approach dependent type theory and natural deduction as special kinds of…