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Monoid and Topological Groupoid
Journal of the Indian Mathematical Society, 2018<p>Here we introduce some new results which are relative to the concept of topological monoid-groupoid and prove that the category of topological monoid coverings of X is equivalent to the category covering groupoids of the monoid-groupoid <span lang="EN-US">&#960;</span><span lang="EN-US"><sub></span>
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Fibrations and topological monoids
2001A 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 +2 more
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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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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, 1984This 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, 1998Let \({\mathcal C}\) 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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D'Alembert's functional equation on topological monoids
Publicationes Mathematicae Debrecen, 2009The author proves that, if \(f\) is a continuous complex-valued function on the topological monoid \(M\) with neutral element \(e\) satisfying the functional equation \[ f(xyz)+f(xzy)=2f(x)f(yz)+2f(y)f(zx)+2f(z)f(xy)-4f(x)f(y)f(z) \] and \(f(e)=1\), then there is a continuous homomorphism \(h:M\rightarrow \text{Mat}_{2}\left(\mathbb{C}\right)\), the ...
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Characterization of a category for monoidal topology
Algebra universalis, 2015This 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, 2006Some 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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Topological materials discovery from crystal symmetry
Nature Reviews Materials, 2021Benjamin J Wieder +2 more
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