scholarly journals On the category of profinite spaces as a reflective subcategory

2013 ◽  
Vol 14 (2) ◽  
Author(s):  
Abolfazl Tarizadeh
Keyword(s):  
Reflective Subcategory

Categories of semigroups in quantum computational structures

2009 ◽  
Vol 59 (4) ◽  
Author(s):  
Hector Freytes ◽  
Antonio Ledda
Keyword(s):  
Fuzzy Logic ◽  
Quantum Computation ◽  
Variety Of Algebras ◽  
Reflective Subcategory ◽  
Mv Algebras ◽  
Computational Structures

AbstractWe investigate a categorial duality between quasi MV-algebras (a variety of algebras arising from quantum computation and tightly connected with fuzzy logic) and a reflective subcategory of l-groups with strong units.

scholarly journals Torsion theories over semihereditary rings

1986 ◽  
Vol 40 (1) ◽  
pp. 54-70 ◽  
Author(s):  
M. W. Evans
Keyword(s):  
Ring Homomorphism ◽  
Torsion Theory ◽  
Dedekind Domain ◽  
Reflective Subcategory ◽  
Flat Modules ◽  
Torsion Theories ◽  
The Right ◽  
Torsion Free ◽  
Regular Rings ◽  
Semihereditary Rings

AbstractIn this paper the class of rings for which the right flat modules form the torsion-free class of a hereditary torsion theory (G, ℱ) are characterized and their structure investigated. These rings are called extended semihereditary rings. It is shown that the class of regular rings with ring homomorphism is a full co-reflective subcategory of the class of extended semihereditary rings with “flat” homomorphisms. A class of prime torsion theories is introduced which determines the torsion theory (G, ℱG). The torsion theory (JG, ℱG) is used to find a suitable generalisation of Dedekind Domain.

A completion-invariant extension of the concept of meet continuous lattices

2015 ◽  
Vol 27 (4) ◽  
pp. 530-539
Author(s):  
WENFENG ZHANG ◽  
XIAOQUAN XU
Keyword(s):  
Heyting Algebra ◽  
Continuous Lattice ◽  
Stable Maps ◽  
Complete Lattices ◽  
Invariant Extension ◽  
Closed Sets ◽  
Reflective Subcategory ◽  
Normal Completion ◽  
Continuous Lattices ◽  
Algebra 2

In this paper, the concept of meet F-continuous posets is introduced. The main results are: (1) A poset P is meet F-continuous iff its normal completion is a meet continuous lattice iff a certain system γ(P) which is, in the case of complete lattices, the lattice of all Scott closed sets is a complete Heyting algebra; (2) A poset P is precontinuous iff P is meet F-continuous and quasiprecontinuous; (3) The category of meet continuous lattices with complete homomorphisms is a full reflective subcategory of the category of meet F-continuous posets with cut-stable maps.

scholarly journals The envelope of a subcategory in topology and group theory

2005 ◽  
Vol 2005 (21) ◽  
pp. 3387-3404 ◽  
Author(s):  
Ahmed Ayache ◽  
Othman Echi
Keyword(s):  
Group Theory ◽  
Reflective Subcategory ◽  
Spectral Spaces

A collection of results are presented which are loosely centered around the notion of reflective subcategory. For example, it is shown that reflective subcategories are orthogonality classes, that the morphisms orthogonal to a reflective subcategory are precisely the morphisms inverted under the reflector, and that each subcategory has a largest “envelope” in the ambient category in which it is reflective. Moreover, known results concerning the envelopes of the category of sober spaces, spectral spaces, and jacspectral spaces, respectively, are summarized and reproved. Finally, attention is focused on the envelopes of one-object subcategories, and examples are considered in the category of groups.

scholarly journals Cubical Sets and Trace Monoid Actions

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Ahmet A. Husainov
Keyword(s):  
Asynchronous Systems ◽  
Adjoint Functors ◽  
Reflective Subcategory ◽  
Cubical Sets ◽  
Higher Dimensional ◽  
Trace Monoid

This paper is devoted to connections between trace monoids and cubical sets. We prove that the category of trace monoids is isomorphic to the category of generalized tori and it is a reflective subcategory of the category of cubical sets. Adjoint functors between the categories of cubical sets and trace monoid actions are constructed. These functors carry independence preserving morphisms in the independence preserving morphisms. This allows us to build adjoint functors between the category of weak asynchronous systems and the category of higher dimensional automata.

ON THE SPECTRALIFICATION OF A HEMISPECTRAL SPACE

2011 ◽  
Vol 10 (04) ◽  
pp. 687-699
Author(s):  
OTHMAN ECHI ◽  
MOHAMED OUELD ABDALLAHI
Keyword(s):  
Topological Space ◽  
Open Subset ◽  
Full Subcategory ◽  
Topological Spaces ◽  
Open Problems ◽  
Complete Answer ◽  
Reflective Subcategory ◽  
Continuous Map ◽  
Open Set ◽  
Spectral Spaces

An open subset U of a topological space X is called intersection compact open, or ICO, if for every compact open set Q of X, U ∩ Q is compact. A continuous map f of topological spaces will be called spectral if f-1 carries ICO sets to ICO sets. Call a topological space Xhemispectral, if the intersection of two ICO sets of X is an ICO. Let HSPEC be the category whose objects are hemispectral spaces and arrows spectral maps. Let SPEC be the full subcategory of HSPEC whose objects are spectral spaces. The main result of this paper proves that SPEC is a reflective subcategory of HSPEC. This gives a complete answer to Problem BST1 of "O. Echi, H. Marzougui and E. Salhi, Problems from the Bizerte–Sfax–Tunis seminar, in Open Problems in Topology II, ed. E. Pearl (Elsevier, 2007), pp. 669–674."

scholarly journals The categorical relationships between neighborhood spaces, ┬-neighborhood spaces and stratified L-neighborhood spaces

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1267-1287
Author(s):  
Lingqiang Li ◽  
Qiu Jin ◽  
Chunxin Bo ◽  
Zhenyu Xiu
Keyword(s):  
Residuated Lattice ◽  
Topological Category ◽  
Reflective Subcategory ◽  
Categorical Properties ◽  
Coreflective Subcategory ◽  
Complete Residuated Lattice

In this paper, for a complete residuated lattice L, we present the categorical properties of ?-neighborhood spaces and their categorical relationships to neighborhood spaces and stratified L-neighborhood spaces. The main results are: (1) the category of ?-neighborhood spaces is a topological category; (2) neighborhood spaces can be embedded in ?-neighborhood spaces as a reflective subcategory, and when L is a meet-continuous complete residuated lattice, ?-neighborhood spaces can be embedded in stratified L-neighborhood spaces as a reflective subcategory; (3) when L is a continuous complete residuated lattice, neighborhood spaces (resp., ?-neighborhood spaces) can be embedded in ?-neighborhood spaces (resp., stratified L-neighborhood spaces) as a simultaneously reflective and coreflective subcategory.

Extensive Subcategories of the Category of T1-spaces

1975 ◽  
Vol 27 (2) ◽  
pp. 311-318 ◽  
Author(s):  
Sung Sa Hong
Keyword(s):  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Reflective Subcategory ◽  
Continuous Maps

It is well known that epimorphisms in the category Top (Top1, respectively) of topological spaces (T1spaces, respectively) and continuous maps are precisely onto continuous maps. Since every mono-reflective subcategory of a category is also epi-reflective and every embedding in Top (Top1, respectively) is a monomorphism, there is no nontrivial reflective subcategory of Top (Top1 respectively) such that every reflection is an embedding. However, in the category Top0 of T0-spaces and continuous maps as well as in the category Haus of Hausdorff spaces and continuous maps, there are epimorphisms which are not onto. Moreover, every reflection of a reflective subcategory of Top0, which contains a non T1-space, is an embedding [16].

Characterizations of M-fuzzifying convex spaces via Galois connections

2021 ◽  
pp. 1-11
Author(s):  
Shao-Yu Zhang
Keyword(s):  
Galois Connection ◽  
Galois Connections ◽  
Reflective Subcategory ◽  
Convex Spaces

This paper introduces a special Galois connection combined with the wedge-below relation. Furthermore, by using this tool, it is shown that the category of M-fuzzifying betweenness spaces and the category of M-fuzzifying convex spaces are isomorphic and the category of arity-2 M-fuzzifying convex spaces can be embedded in the category of M-fuzzifying interval spaces as a reflective subcategory.

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