Related papers: On categories of o-minimal structures
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
In this paper we discuss various philosophical aspects of the hyperstructure concept extending networks and higher categories. By this discussion we hope to pave the way for applications and further developments of the mathematical theory…
In this paper, we analyze and compare three of the many algebraic structures that have been used for modeling dependent type theories: categories with families, split type-categories, and representable maps of presheaves. We study these in…
We generalize the notion of a modified trace (or m-trace) to the setting of non-unimodular categories. M-traces are known to play an important role in low-dimensional topology and representation theory, as well as in studying the category…
Transfer learning methods endeavor to leverage relevant knowledge from existing source pre-trained models or datasets to solve downstream target tasks. With the increase in the scale and quantity of available pre-trained models nowadays, it…
Many modern learning tasks require models that can take inputs of varying sizes. Consequently, dimension-independent architectures have been proposed for domains where the inputs are graphs, sets, and point clouds. Recent work on graph…
In these lecture notes, we give a brief introduction to some elements of category theory. The choice of topics is guided by applications to functional programming. Firstly, we study initial algebras, which provide a mathematical…
We introduce basic notions in category theory to type theorists, including comprehension categories, categories with attributes, contextual categories, type categories, and categories with families along with additional discussions that are…
This paper deals with fractional-order controlled systems and fractional-order controllers in the frequency domain. The mathematical description by fractional transfer functions and properties of these systems are presented. The new ways…
This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also…
In this paper we generalize a shift theorem, which plays a key role in studying representations of FI$^m$, the product category of the category of finite sets and injections, and classify finitely generated injective FI$^m$-modules over a…
The aim of this paper is to give a unifying description of various constructions (subanalytic, semialgebraic, o-minimal site) using the notion of T-topology. We then study the category of T-sheaves.
In this article we prove various results about transferring or lifting $\mathrm{A}_\infty$-algebra structures along quasi-isomorphisms over a commutative ring.
We build a model structure from the simple point of departure of a structured interval in a monoidal category - more generally, a structured cylinder and a structured co-cylinder in a category.
Motivated by the analysis and geometry of metric-measure structures in infinite dimensions, we study the category of extended metric-topological spaces, along with many of its distinguished subcategories (such as the one of compact spaces).…
This paper studies the existence of model category structures on algebras and modules over operads in monoidal model categories.
Category theory has become central to certain aspects of theoretical physics. Bain [Synthese, 190:1621--1635 (2013)] has recently argued that this has significance for ontic structural realism. We argue against this claim. In so doing, we…
We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.
Let R be an o-minimal field with a proper convex subring V. We axiomatize the class of all structures (R,V) such that k_ind, the corresponding residue field with structure induced from R via the residue map, is o-minimal. More precisely, in…
The growing complexity of modern practical problems puts high demands on the mathematical modelling. Given that various models can be used for modelling one physical phenomenon, the role of model comparison and model choice becomes…