scholarly journals Reflective Full Subcategories of the Category ofL-Posets

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
Hongping Liu ◽  
Qingguo Li ◽  
Xiangnan Zhou
Keyword(s):  
Special Class ◽  
Full Subcategory ◽  
Closure Operators ◽  
The Relationship ◽  
Equivalent Description

This paper focuses on the relationship betweenL-posets and completeL-lattices from the categorical view. By considering a special class of fuzzy closure operators, we prove that the category of completeL-lattices is a reflective full subcategory of the category ofL-posets with appropriate morphisms. Moreover, we characterize the Dedekind-MacNeille completions ofL-posets and provide an equivalent description for them.

scholarly journals Reflective subcategories

2000 ◽  
Vol 42 (1) ◽  
pp. 97-113 ◽  
Author(s):  
Juan Rada ◽  
Manuel Saorín ◽  
Alberto del Valle
Keyword(s):  
Category Theory ◽  
Full Subcategory ◽  
Subject Classification ◽  
Adjoint Functor ◽  
Direct Limits ◽  
The Relationship ◽  
Good Behaviour

Given a full subcategory [Fscr ] of a category [Ascr ], the existence of left [Fscr ]-approximations (or [Fscr ]-preenvelopes) completing diagrams in a unique way is equivalent to the fact that [Fscr ] is reflective in [Ascr ], in the classical terminology of category theory.In the first part of the paper we establish, for a rather general [Ascr ], the relationship between reflectivity and covariant finiteness of [Fscr ] in [Ascr ], and generalize Freyd's adjoint functor theorem (for inclusion functors) to not necessarily complete categories. Also, we study the good behaviour of reflections with respect to direct limits. Most results in this part are dualizable, thus providing corresponding versions for coreflective subcategories.In the second half of the paper we give several examples of reflective subcategories of abelian and module categories, mainly of subcategories of the form Copres (M) and Add (M). The second case covers the study of all covariantly finite, generalized Krull-Schmidt subcategories of {\rm Mod}_{R}, and has some connections with the “pure-semisimple conjecture”.1991 Mathematics Subject Classification 18A40, 16D90, 16E70.

scholarly journals Neighbourhood lattices – a poset approach to topological spaces

1989 ◽  
Vol 39 (1) ◽  
pp. 31-48 ◽  
Author(s):  
Frank P. Prokop
Keyword(s):  
Topological Space ◽  
Lattice Structure ◽  
Algebraic Closure ◽  
Topological Spaces ◽  
Closure Operators ◽  
Continuity Properties ◽  
Image Function ◽  
Topological Closure ◽  
Arbitrary Lattice ◽  
The Relationship

In this paper neighbourhood lattices are developed as a generalisation of topological spaces in order to examine to what extent the concepts of “openness”, “closedness”, and “continuity” defined in topological spaces depend on the lattice structure of P(X), the power set of X.A general pre-neighbourhood system, which satisfies the poset analogues of the neighbourhood system of points in a topological space, is defined on an ∧-semi-lattice, and is used to define open elements. Neighbourhood systems, which satisfy the poset analogues of the neighbourhood system of sets in a topological space, are introduced and it is shown that it is the conditionally complete atomistic structure of P(X) which determines the extension of pre-neighbourhoods of points to the neighbourhoods of sets.The duals of pre-neighbourhood systems are used to generate closed elements in an arbitrary lattice, independently of closure operators or complementation. These dual systems then form the backdrop for a brief discussion of the relationship between preneighbourhood systems, topological closure operators, algebraic closure operators, and Čech closure operators.Continuity is defined for functions between neighbourhood lattices, and it is proved that a function f: X → Y between topological spaces is continuous if and only if corresponding direct image function between the neighbourhood lattices P(X) and P(Y) is continuous in the neighbourhood sense. Further, it is shown that the algebraic character of continuity, that is, the non-convergence aspects, depends only on the properites of pre-neighbourhood systems. This observation leads to a discussion of the continuity properties of residuated mappings. Finally, the topological properties of normality and regularity are characterised in terms of the continuity properties of the closure operator on a topological space.

Triple Cyclic Codes Over 𝔽q + u𝔽q

2021 ◽  
pp. 1-21
Author(s):  
Ting Yao ◽  
Shixin Zhu ◽  
Binbin Pang
Keyword(s):  
Special Class ◽  
Linear Codes ◽  
Cyclic Code ◽  
Cyclic Codes ◽  
Cyclic Shift ◽  
Generating Sets ◽  
Optimal Linear ◽  
Number Formula ◽  
The Relationship ◽  
Optimal Linear Codes

Let [Formula: see text], where [Formula: see text] is a power of a prime number [Formula: see text] and [Formula: see text]. A triple cyclic code of length [Formula: see text] over [Formula: see text] is a set that can be partitioned into three parts that any cyclic shift of the coordinates of the three parts leaves the code invariant. These codes can be viewed as [Formula: see text]-submodules of [Formula: see text]. In this paper, we study the generator polynomials and the minimum generating sets of this kind of codes. Some optimal or almost optimal linear codes are obtained from this family of codes. We present the relationship between the generators of triple cyclic codes and their duals. As a special class of triple cyclic codes, separable codes over [Formula: see text] are discussed briefly in the end.

Orderings and signatures of higher level on multirings and hyperfields

2012 ◽  
Vol 10 (3) ◽  
pp. 489-518 ◽  
Author(s):  
Paweł Gładki ◽  
Murray Marshall
Keyword(s):  
Full Subcategory ◽  
First Order ◽  
The Relationship

AbstractMultirings are objects like rings but with multi-valued addition. In the present paper we extend results of E. Becker and others concerning orderings of higher level on fields and rings to orderings of higher level on hyperfields and multirings and, in the process of doing this, we establish higher level analogs of the results previously obtained by the second author. In particular, we introduce a class of multirings called ℓ-real reduced multirings, define a natural reflection A ⇝ Qℓ-red(A) from the category of multirings satisfying to the full subcategory of ℓ-real reduced multirings, and provide an elementary first-order description of these objects. The relationship between ℓ-real reduced hyperfields and the spaces of signatures defined by Mulcahy and Powers is also examined.

The Relationship of Early Special Class lacement and the Self-Concepts of Mentally Handicapped Children

1966 ◽  
Vol 33 (2) ◽  
pp. 77-81 ◽  
Author(s):  
C. Lamar Mayer
Keyword(s):  
High School ◽  
Junior High School ◽  
Special Class ◽  
The Self ◽  
Self Concept ◽  
School Age ◽  
Mentally Handicapped ◽  
Handicapped Children ◽  
Relationship Of ◽  
The Relationship

Ninety-eight mentally handicapped students of junior high school age were grouped according to time of placement in a special class. Self-concept ratings were obtained to evaluate the relationship of time of placement in a special class and self-concept. The relationship of self-concept to CA, MA, and sex was also investigated.

The Morbid Psychology of Criminals

1874 ◽  
Vol 20 (90) ◽  
pp. 167-185 ◽  
Author(s):  
David Nicolson
Keyword(s):  
Special Class ◽  
Mental Condition ◽  
The Relationship

Is a given prisoner fit, so far as his mental condition is concerned, to undergo the discipline to which his sentence of imprisonment commits him? The relationship existing between the mental constitution of prisoners, and the active and passive penalties which go to make up their prison experience, requires some notice before we can recognise how a special class of weak-minded criminals arises apart from those who are positively insane.

A Schur-Type Factorization of Central Extended Matrix

2014 ◽  
Vol 496-500 ◽  
pp. 2011-2014
Author(s):  
Li Yang ◽  
Cheng Feng Xu
Keyword(s):  
Special Class ◽  
Centrosymmetric Matrix ◽  
Relationship Of ◽  
The Relationship ◽  
Extended Matrix

In this paper, we study the Schur factorization of a special class of centrosymmetric matrices: the central extended matrix which is not only a centrosymmetric matrix but also a row extended matrix. The formula for the Schur-type factorization is obtained, and the relationship of the central extended matrix with mother matrix is also obtained.

scholarly journals Freely adjoining monoidal duals

2020 ◽  
pp. 1-21
Author(s):  
Kevin Coulembier ◽  
Ross Street ◽  
Michel van den Bergh
Keyword(s):  
Full Subcategory ◽  
Monoidal Category ◽  
Dual Pair ◽  
Explicit Model ◽  
Monoidal Categories ◽  
Monoidal Functor ◽  
Simplicial Category ◽  
Combinatorial Model ◽  
The Relationship ◽  
Distinguished Object

Abstract Given a monoidal category $\mathcal C$ with an object J, we construct a monoidal category $\mathcal C[{J^ \vee }]$ by freely adjoining a right dual ${J^ \vee }$ to J. We show that the canonical strong monoidal functor $\Omega :\mathcal C \to \mathcal C[{J^ \vee }]$ provides the unit for a biadjunction with the forgetful 2-functor from the 2-category of monoidal categories with a distinguished dual pair to the 2-category of monoidal categories with a distinguished object. We show that $\Omega :\mathcal C \to \mathcal C[{J^ \vee }]$ is fully faithful and provide coend formulas for homs of the form $\mathcal C[{J^ \vee }](U,\,\Omega A)$ and $\mathcal C[{J^ \vee }](\Omega A,U)$ for $A \in \mathcal C$ and $U \in \mathcal C[{J^ \vee }]$ . If ${\rm{N}}$ denotes the free strict monoidal category on a single generating object 1, then ${\rm{N[}}{{\rm{1}}^ \vee }{\rm{]}}$ is the free monoidal category Dpr containing a dual pair – ˧ + of objects. As we have the monoidal pseudopushout $\mathcal C[{J^ \vee }] \simeq {\rm{Dpr}}{{\rm{ + }}_{\rm{N}}}\mathcal C$ , it is of interest to have an explicit model of Dpr: we provide both geometric and combinatorial models. We show that the (algebraist’s) simplicial category Δ is a monoidal full subcategory of Dpr and explain the relationship with the free 2-category Adj containing an adjunction. We describe a generalization of Dpr which includes, for example, a combinatorial model Dseq for the free monoidal category containing a duality sequence X0 ˧ X1 ˧ X2 ˧ … of objects. Actually, Dpr is a monoidal full subcategory of Dseq.

Psychological Needs and Preferences for Teaching Exceptional Children

1966 ◽  
Vol 32 (5) ◽  
pp. 313-324 ◽  
Author(s):  
Reginald L. Jones ◽  
Nathan W. Gottfried
Keyword(s):  
Special Class ◽  
Psychological Needs ◽  
Special Education Students ◽  
Education Students ◽  
Exceptional Children ◽  
Personality Variables ◽  
Edwards Personal Preference Schedule ◽  
Teacher Preference ◽  
The Relationship ◽  
Representative Samples

The relationship between psychological needs (as reflected by the Edwards Personal Preference Schedule and the Teacher Preference Schedule) and preferences for teaching certain exceptional children was studied in a sample of 534 regular and special education students and 192 practicing regular and special class teachers. A number of personality variables related to preferences for teaching certain exceptionalities were identified. The small numbers preferring to teach any one exceptionality and the failure in most instances to confirm the results across subject populations suggested the need for replication of the present study using larger and more representative samples of subjects.

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