Related papers: Fra\"iss\'e sequences: category-theoretic approach…
Categorification is the process of finding category-theoretic analogs of set-theoretic concepts by replacing sets with categories, functions with functors, and equations between functions by natural isomorphisms between functors, which in…
This paper develops a categorical framework to clarify the relationship between the completeness and compactness theorems in classical first-order logic. Rather than claiming that different model constructions yield naturally isomorphic…
This paper investigates advanced notions of lineability and spaceability within the frameworks of sequence spaces and operator ideals. We propose the notion of \emph{Standard Sequence Classes} to provide an environment that unifies numerous…
The concept of process is ubiquitous in science, engineering and everyday life. Category theory, and monoidal categories in particular, provide an abstract framework for modelling processes of many kinds. In this paper, we concentrate on…
Category theory is the language of homological algebra, allowing us to state broadly applicable theorems and results without needing to specify the details for every instance of analogous objects. However, authors often stray from the realm…
This is an introduction to the study of abstract homotopy theory by means of model categories and $(\infty,1)$-categories. The only prerequisites are very basic general topology and abstract algebra. None categorical background is needed.…
In this paper we look at the notion of cohomological triviality of fibrations of homogeneous spaces of affine algebraic groups defined over $\mathbb{C}$ and use topological methods, primarily the theory of covering spaces. This is made…
We introduce an abstract concept of quantum field theory on categories fibered in groupoids over the category of spacetimes. This provides us with a general and flexible framework to study quantum field theories defined on spacetimes with…
We review the problem of finding a general framework within which one can construct quantum theories of non-standard models for space, or space-time. The starting point is the observation that entities of this type can typically be regarded…
We devise a fairly general sufficient condition ensuring that the endomorphism monoid of a countably infinite ultrahomogeneous structure (i.e. a Fra\"{\i}ss\'{e} limit) embeds all countable semigroups. This approach provides us not only…
We introduce the concept of a homogeneity supermanifold, which is, roughly speaking, a supermanifold equipped with a privileged atlas whose coordinates carry prescribed (real) homogeneity degrees. This structure defines a sheaf of graded…
We provide a self-contained introduction to the classical theory of universal-homogeneous models (also known as generic structures, rich models, or Fra\"iss\'e limits). In the literature, most treatments restrict consideration to embeddings…
In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…
We discuss homogeneity and universality issues in the theory of abstract linear spaces, namely, structures with points and lines satisfying natural axioms, as in Euclidean or projective geometry. We show that the two smallest projective…
We present a construction that allows us to define a limit object of Banach space decorated graph sequences in a generalized homomorphism density sense. This general functional analytic framework provides a universal language for various…
We present an intrinsic and concrete development of the subdivision of small categories, give some simple examples and derive its fundamental properties. As an application, we deduce an alternative way to compare the homotopy categories of…
Category Theory provides us with a clear notion of what is an internal structure. This will allow us to focus our attention on a certain type of relationship between context and structure.
This paper presents preliminary work on a general system for integrating dependent types into substructural type systems such as linear logic and linear type theory. Prior work on this front has generally managed to deliver type systems…
Homotopy connectedness theorems for complex submanifolds of homogeneous spaces (sometimes referred to as theorems of Barth-Lefshetz type) have been established by a number of authors. Morse Theory on the space of paths lead to an elegant…
The modern theory of homogeneous structures begins with the work of Roland Fra\"iss\'e. The theory developed in the last seventy years is placed in the border area between combinatorics, model theory, algebra, and analysis. We turn our…