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 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 A Category Theoretic Approach to Metaphor Comprehension: Theory of Indeterminate Natural Transformation

2020 ◽  
Author(s):  
Miho Fuyama ◽  
Hayato Saigo ◽  
Tatsuji Takahashi
Keyword(s):  
Category Theory ◽  
Natural Transformation ◽  
Mathematical Structure ◽  
Theoretic Approach ◽  
Metaphor Comprehension ◽  
Central Notion ◽  
Meaning Creation ◽  
Natural Transformations ◽  
Categories And Functors ◽  
The Relationship

We propose the theory of indeterminate natural transformation (TINT) to investigate the dynamical creation of meaning as an association relationship between images, focusing on metaphor comprehension as an example. TINT models meaning creation as a type of stochastic process based on mathematical structure and defined by association relationships, such as morphisms in category theory, to represent the indeterminate nature of structure-structure interactions between the systems of image meanings. Such interactions are formulated in terms of the so-called coslice categories and functors as structure-preserving correspondences between them. The relationship between such functors is “indeterminate natural transformation”, the central notion in TINT, which models the creation of meanings in a precise manner. For instance, metaphor comprehension is modeled by the construction of indeterminate natural transformations from a canonically defined functor, which we call the base-of-metaphor functor.

scholarly journals On -Quasi Irresolute Functions

2017 ◽  
Vol 1 (2) ◽  
pp. 72-77
Author(s):  
C. Janaki ◽  
Ganes M. Pandya
Keyword(s):  
Subject Classification ◽  
New Class ◽  
2000 Mathematics Subject Classification ◽  
The Relationship ◽  
Class Of Functions

In this paper we introduce a new class of functions called -quasi irresolute functions. The notion of -quasi graphs are introduced and the relationship between -quasi irresolute functions and -quasi closed graphs is analysed. 2000 Mathematics Subject Classification : 54C08, 54C10.

scholarly journals Stylistic Devices in The Schoole of Vertue, an Early Modern Manual of Good Conduct for Children

2016 ◽  
Vol 51 (3) ◽  
pp. 95-124
Author(s):  
Hanna Rutkowska
Keyword(s):  
Early Modern ◽  
Literary Texts ◽  
Second Person ◽  
Emotional Closeness ◽  
Rhetorical Device ◽  
Rhetorical Devices ◽  
Early Modern English ◽  
The Relationship ◽  
Good Behaviour

Abstract This paper is a case study examining the choice and interaction of stylistic devices employed in The Schoole of Vertue, Francis Segar and Robert Crowley’s manual of good manners for children issued between 1582 and 1687. It was designed to convince its readers that particular patterns of behaviour were socially beneficial and worth following. In order to enhance the attractiveness, persuasiveness, and mnemonic qualities of the text, several stylistic devices are employed in the manual, including, for example, rhymes, acronyms, as well as binomials. It is generally agreed that repetitive patterns (especially binomials) are typical of formal registers, and particularly plentiful in legal and literary texts in Early Modern English, but the present study shows that similar rhetorical devices were also readily employed in the less formal and elevated style of manuals of good behaviour. Another rhetorical device frequently used in the manual under consideration consists in addressing the reader directly with the second person singular pronoun, especially in imperative constructions, thus creating an ambiance of emotional closeness, characterising the relationship between the master and the pupil.

scholarly journals On the relationship between ordinary thin sets and full-thin sets

1980 ◽  
Vol 29 (3) ◽  
pp. 348-361
Author(s):  
J. S. Hwang ◽  
H. L. Jackson
Keyword(s):  
Unit Ball ◽  
Half Space ◽  
Boundary Point ◽  
Subject Classification ◽  
Thin Set ◽  
Thin Sets ◽  
The Relationship

AbstractIn this work we demonstrate that if Ω ⊂ Rn (n ≧ 3) is either a half space or a unit ball, and if E ⊂ ω then E is an ordinary thin set at a boundary point of Ω (including the point at infinity if Ω is a half space) if and only if it is a full-thin set at the corresponding Kuramochi boundary point of Ω. The case for n = 2 has already been considered in an earlier work.1980 Mathematics subject classification (Amer. Math. Soc.): 31 B 05.

On Measures of Affinity for Truncated Distributions

2007 ◽  
Vol 59 (3-4) ◽  
pp. 151-162
Author(s):  
S. Smitha ◽  
K. R. Muraleedharan Nair ◽  
P. G. Sankaran
Keyword(s):  
Functional Form ◽  
Hazard Model ◽  
Subject Classification ◽  
Proportional Hazard ◽  
Proportional Hazard Model ◽  
Characterization Result ◽  
Truncated Distributions ◽  
Relationship Of ◽  
The Relationship

Abstract: In the present paper we define affinity for truncated distributions and examine its properties. The relationship of this measure with other discrimination measures is examined. We also provide a characterization result for the proportional hazard model using the functional form of the truncated affinity. AMS (2000) Subject Classification: 62E10, 90B25

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.

scholarly journals Badiou and the Ontological Limits of Mathematics

2020 ◽  
Vol 41 (2) ◽  
Author(s):  
Michael Hauser
Keyword(s):  
Set Theory ◽  
Category Theory ◽  
Layered Model ◽  
And Mathematics ◽  
The One ◽  
The Relationship

I propose to depict the relationship between Badiou’s philosophy and mathematics as a three-layered model. Philosophy as metaontology creates a metastructure, mathematics as ontology in the form of a condition of philosophy constitutes its situation, and mathematics as a multiple universe of all given axioms, theorems, techniques, interpretations, and systems (set theory, category theory, etc.) is an inconsistent multiplicity. So, we can interpret the relationship between philosophy and mathematics as the one between a metastructure and a situation. By using Easton’s theorem, we come to realise that philosophical concepts in the metastructure “quantitatively” exceed the elements that belong to mathematics as ontology. Therefore, philosophy as metaontology shows the limits of mathematics as ontology.

scholarly journals Semigroups for flows on limits of graphs

2021 ◽  
Vol 58 ◽  
pp. 7-21
Author(s):  
Christian Budde
Keyword(s):  
Category Theory ◽  
Approximation Theorem ◽  
Strongly Continuous Semigroups ◽  
Growing Networks ◽  
Direct Limits ◽  
Abstract Notion

We use a version of the Trotter-Kato approximation theorem for strongly continuous semigroups in order to study ows on growing networks. For that reason we use the abstract notion of direct limits in the sense of category theory

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