Results 181 to 190 of about 354,525 (216)

Fibrations and topological monoids

2001
A continuous map p: X → Y has the lifting property with respect to a pair of topological spaces (Z, A) if for every commutative diagram of the form there exists a continuous map \(\Bbbk \) : Z → X such that pk = g and ki = f.
Yves Félix, Stephen Halperin, Jean-Claude Thomas   +2 more
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Topological Types of Convergence for Nets of Multifunctions

International Journal of Topology
This article proposes a unified concept of topological types of convergence for nets of multifunctions between topological spaces. Any kind of convergence is representable by a (2n + 2)-tuple, n = 0, 1, …, of two special functions u and l, such that ...
Marian Przemski
semanticscholar   +1 more source

On topological and algebraic structures of categorical random variables

arXiv.org
Based on entropy and symmetrical uncertainty (SU), we define a metric for categorical random variables and show that this metric can be promoted into an appropriate quotient space of categorical random variables.
Inocencio Ortiz, Santiago G'omez-Guerrero, C. Schaerer   +2 more
semanticscholar   +1 more source

Monoidal Topology

2014
Monoidal Topology describes an active research area that, after various past proposals on how to axiomatize 'spaces' in terms of convergence, began to emerge at the beginning of the millennium. It combines Barr's relational presentation of topological spaces in terms of ultrafilter convergence with Lawvere's interpretation of metric spaces as small ...
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Classifying Spaces of Topological Monoids and Categories

American Journal of Mathematics, 1984
This article explores homology and weak homotopy equivalences between classifying spaces of topological categories and discrete categories. Many recent results have dealt with this phenomenon: e.g. for any space X there is a discrete group and a homology equivalence BG\(\to X\) [\textit{D. Kan} and \textit{W.
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Topological Hopf Algebras and Braided Monoidal Categories

Applied Categorical Structures, 1998
Let \({\mathcal C}\) be a small monoidal category, \(K\) a Dedekind domain. The author first notes that any exact faithful monoidal functor from \({\mathcal C}\) to the category of finite rank projective \(K\)-modules factors through a functor from \({\mathcal C}\) to the category of continuous modules over a topological \(K\)-bialgebra \(A\).
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Characterization of a category for monoidal topology

Algebra universalis, 2015
This paper presents a characterization of the category of preordered sets and monotone maps that is similar to that of the category of topological spaces and continuous maps in terms of the Sierpinski object (Theorem 2.10), then the author lifts the characterization to the quantale-valued setting (Theorem 5.10).
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Retractions and retracts of free topological monoids

International Journal of Computer Mathematics, 2006
Some topological properties of retracts, semiretracts and retractions which make a link between the topological notion of a retract with its pure algebraic analogon in free monoids are presented.
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ON FREE AND PROJECTIVE S-SPACES AND FLOWS OVER A TOPOLOGICAL MONOID

, 2010
B. Khosravi
semanticscholar   +1 more source

Topological actions of Temperley–Lieb monoids and representation stability

Journal of Algebra and Its Applications
In this paper, we consider the Temperley–Lieb algebras [Formula: see text] at [Formula: see text]. Since [Formula: see text], we can consider the multiplicative monoid structure and ask how this monoid acts on topological spaces. Given a monoid action on a topological space, we get an algebra action on each homology group.
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