Drinfel’d construction for Hom–Hopf T-coalgebras

2020 ◽  
Vol 31 (08) ◽  
pp. 2050058
Author(s):  
Dongdong Yan ◽  
Shuanhong Wang
Keyword(s):  
Full Subcategory ◽  
Module Category ◽  
Triangular Structure ◽  
Equivalent Relation ◽  
Hopf Formula

Let [Formula: see text] be a Hom–Hopf T-coalgebra over a group [Formula: see text] (i.e. a crossed Hom–Hopf [Formula: see text]-coalgebra). First, we introduce and study the left–right [Formula: see text]-Yetter–Drinfel’d category [Formula: see text] over [Formula: see text], with [Formula: see text], and construct a class of new braided T-categories. Then, we prove that a Yetter–Drinfel’d module category [Formula: see text] is a full subcategory of the center [Formula: see text] of the category of representations of [Formula: see text]. Next, we define the quasi-triangular structure of [Formula: see text] and show that the representation crossed category [Formula: see text] is quasi-braided. Finally, the Drinfel’d construction [Formula: see text] of [Formula: see text] is constructed, and an equivalent relation between [Formula: see text] and the representation of [Formula: see text] is given.

scholarly journals Recollements, comma categories and morphic enhancements

2021 ◽  
pp. 1-25
Author(s):  
Xiao-Wu Chen ◽  
Jue Le
Keyword(s):  
Module Category ◽  
Triangulated Category ◽  
Triangulated Categories ◽  
Comma Category ◽  
The Right ◽  
Projective Lines ◽  
Triangle Functor

For each recollement of triangulated categories, there is an epivalence between the middle category and the comma category associated with a triangle functor from the category on the right to the category on the left. For a morphic enhancement of a triangulated category $\mathcal {T}$ , there are three explicit ideals of the enhancing category, whose corresponding factor categories are all equivalent to the module category over $\mathcal {T}$ . Examples related to inflation categories and weighted projective lines are discussed.

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.

Topological tools for the prescribed scalar curvature problem on S n

2014 ◽  
Vol 12 (12) ◽  
Author(s):  
Dina Abuzaid ◽  
Randa Ben Mahmoud ◽  
Hichem Chtioui ◽  
Afef Rigane
Keyword(s):  
Scalar Curvature ◽  
Conformal Metrics ◽  
Standard Sphere ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Hopf Formula ◽  
Curvature Problem ◽  
Formula Type

AbstractIn this paper, we consider the problem of the existence of conformal metrics with prescribed scalar curvature on the standard sphere S n, n ≥ 3. We give new existence and multiplicity results based on a new Euler-Hopf formula type. Our argument also has the advantage of extending well known results due to Y. Li [16].

A Note on the Radical of a Module Category

2013 ◽  
Vol 41 (12) ◽  
pp. 4419-4424 ◽  
Author(s):  
Claudia Chaio ◽  
Shiping Liu
Keyword(s):  
Module Category

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.

Analog Control of Continuous Copper Wire Annealing Based on Temperature Detecting

2014 ◽  
Vol 487 ◽  
pp. 591-594
Author(s):  
Yong Zhong Lin ◽  
Xue Jun Xu ◽  
Hong Yang Sun ◽  
Zuan Zhen Lu ◽  
Cheng Gang Wang
Keyword(s):  
Annealing Temperature ◽  
Analog Circuit ◽  
Copper Wire ◽  
Temperature Deviation ◽  
Linear Fitting ◽  
Equivalent Relation ◽  
Analog Control

The paper acquires the equivalent relation between the velocity of wires and annealing temperature through deduction, based on the measurement of the annealing temperature. A controller characterizing annealing temperature could be inserted before the traditional PI annealing controller, so that annealing temperature could be controlled while the annealing temperature deviation is simulated by the error of the velocity of wires. In the paper, a kind of analog circuit is chosen to achieve the equivalent relation between the velocity of wires and annealing temperature by linear fitting under the condition of preciseness.

Linear types and approximation

2000 ◽  
Vol 10 (6) ◽  
pp. 719-745 ◽  
Author(s):  
MICHAEL HUTH ◽  
ACHIM JUNG ◽  
KLAUS KEIMEL
Keyword(s):  
Full Subcategory ◽  
Linear Logic ◽  
Domain Theory ◽  
Classical Domain ◽  
Complete Distributivity ◽  
Linear Types ◽  
Continuous Lattices

We study continuous lattices with maps that preserve all suprema rather than only directed ones. We introduce the (full) subcategory of FS-lattices, which turns out to be *-autonomous, and in fact maximal with this property. FS-lattices are studied in the presence of distributivity and algebraicity. The theory is extremely rich with numerous connections to classical Domain Theory, complete distributivity, Topology and models of Linear Logic.

Überlegungen zu einer neu entdeckten Architekturzeichnung Michelangelos

Architectura ◽  
2019 ◽  
Vol 49 (1) ◽  
pp. 24-44
Author(s):  
Otfried Garbe
Keyword(s):  
Square Root ◽  
Reading Room ◽  
Architectural Drawing ◽  
Triangular Structure

Abstract The author presents a newly discovered architectural drawing which shows one of the two identical portals in the reading room of the Biblioteca Laurenziana in Florence. The drawing is attributed to Michelangelo by the author and compared with two other drawings by the artist, one of which connects the Cloister with the vestibule of the Library and another that leads from the vestibule to the reading room. The present drawing has close visual similarities with both the drawings generally accepted as Michelangelo’s. However, it is distinguished by a double pediment that combines a triangular structure with a rounded one. In addition, it is designed in a perspectival manner that takes into account the depth of the opening and of its pediment. All three drawings have the same overall proportions, corresponding to the ›divina proportione‹. The openings in the three drawings have a quotient that is identical with the square root of five. The handwriting within the opening appears to be identical with Michelangelo’s hand.

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