• Korean Journal of Mathematics
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• v.26 no.3
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• pp.439-458
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• 2018

In this study, we interpret the notion of homotopy of morphisms in the category of crossed modules in a category C of groups with operations using the categorical equivalence between the categories of crossed modules and of internal categories in C. Further, we characterize the derivations of crossed modules in a category C and obtain new crossed modules using regular derivations of old one.

• Journal of the Chungcheong Mathematical Society
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• v.6 no.1
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• pp.45-52
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• 1993

In this paper, we obtain the internal function space structure in the category of the fibrewise convergence spaces by means of the final structure. Moreover, we investigate cartesian closedness of the category of fibrewise convergence spaces which contains the category of fibrewise topological spaces as a full subcategory.

• Communications of the Korean Mathematical Society
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• v.27 no.1
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• pp.23-36
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• 2012

Dual monoidal category $\mathcal{C}^*$ of a monoidal functor F : $\mathcal{C}\;{\rightarrow}\;\mathcal{V}$ has been constructed by S. Majid. In this paper, we extend the construction of dual structures for an Ann-functor F : $\mathcal{B}\;{\rightarrow}\;\mathcal{A}$. In particular, when F = $id_{\mathcal{A}}$, then the dual category $\mathcal{A}^*$ is indeed the center of $\mathcal{A}$ an this is a braided Ann-category.

• Journal of the Korean Mathematical Society
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• v.56 no.3
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• pp.623-644
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• 2019

We investigate the homotopy category ${\mathcal{K}}_N(Inj{\mathfrak{A}})$ of N-complexes of injectives in a Grothendieck abelian category ${\mathfrak{A}}$ not necessarily locally noetherian, and prove that the inclusion ${\mathcal{K}}_N(Inj{\mathfrak{A}}){\rightarrow}{\mathcal{K}}({\mathfrak{A}})$ has a left adjoint and ${\mathcal{K}}_N(Inj{\mathfrak{A}})$ is well generated. We also show that the homotopy category ${\mathcal{K}}_N(PrjR)$ of N-complexes of projectives is compactly generated whenever R is right coherent.

• Journal of the Korean Mathematical Society
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• v.59 no.1
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• pp.171-192
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• 2022

For any category with a distinguished collection of sequences, such as n-exangulated category, category of N-complexes and category of precomplexes, we consider its Grothendieck group and similar results of Bergh-Thaule for n-angulated categories [1] are proven. A classification result of dense complete subcategories is given and we give a formal definition of K-groups for these categories following Grayson's algebraic approach of K-theory for exact categories [4].

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.05a
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• pp.37-40
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• 2003

We introduce the category IRel (H) consisting of intuitionistic fuzzy relational spaces on sets and we study structures of the category IRel (H) in the viewpoint of the topological universe introduced by L.D.Nel. Thus we show that IRel (H) satisfies all the conditions of a topological universe over Set except the terminal separator property and IRel (H) is cartesian closed over Set.

• Journal of the Korean Institute of Intelligent Systems
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• v.2 no.3
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• pp.17-21
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• 1992

In this paper we consider the notion of fuzzy relation as a generalization of that of fuzzy set. For a complete Heyting algebra L. the category set(L) of all L-fuzzy sets is shown to be a bireflective subcategory of the category Rel(L) of all L-fuzzy relations and L-fuzzy relation preserving maps. We investigate categorical structures of subcategories of Rel(L) in view of quasitopos. Among those categories, we include the category L-fuzzy similarity relations with respect to both max-min and max-product compositions, respectively, as a cartesian closed topological category. Moreover, we describe exponential objects explicitly in terms of function space.

• Honam Mathematical Journal
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• v.45 no.2
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• pp.269-284
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• 2023

In this paper we study generalizations of the concept of pure-direct-projectivity from module categories to Grothendieck categories. We examine for which categories or under what conditions pure-direct-projective objects are direct-projective, quasi-projective, pure-projective, projective and flat. We investigate classes all of whose objects are pure-direct-projective. We give applications of some of the results to comodule categories.

• Journal of Dental Rehabilitation and Applied Science
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• v.24 no.2
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• pp.203-211
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• 2008

Minimizing damage to anatomical structure is a prerequisite for skeletal anchorage system to install a miniscrew. This research has focused on evaluating the stability and safety of installation in the maxillary molar buccal area, in which most miniscrews are installed clinically and initial fixation is weak. CT (computerized tomography)images were taken for surveying the possibility of damaging to adjucent teeth in accordance with installation angle. If we install a mini-screw($1.2{\times}6.0mm$) in the maxillary molar buccal area, it would be located generally in the 5~8mm upper of CEJ and 3~5mm inner of the cortical bone surface. We has measured the space between roots And comparison has been made for gender and the space between roots in accordance with the 3 different angles of installation(30 degree, 40 degree, 60 degree) in 3 categories. Category 1 : between 1st molar and 2nd molar Category 2 : between 1st molar and 2nd premolar Category 3 : between 1st premolar and 2nd premolar The result are as follow; 1. The space for category 1 was significantly small. 2. For the installation angle, it was safer to install with steeper angle in category 1 and category 2, but not in category 3. According to these results, the installation a miniscrew in category 2, 3 is safer than in category 1. And it is safer to install with steeper angle in category 1 and category 2.

• Journal of Digital Convergence
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• v.10 no.11
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• pp.551-558
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• 2012

Objectives: The purpose of this study was to determine whether the sacrooccipital category II blocking technique may improve abdominal muscle endurance and alleviate shoulder pain caused by pelvic tilting. Methods: A total of 50 subjects diagnosed with category II sacroiliac joint instability and lower back pain were randomly assigned to the control or treatment group. The sacrooccipital technique category II blocking procedure (2-min duration) was performed 3 times a week until the category II indicator of joint instability had subsided. The control subjects were subjected to a sham procedure of equal duration and frequency. We assessed abdominal muscle endurance using the partial curl-up test and shoulder pain using a visual analogue scale, before and immediately after the intervention and 2 weeks after the intervention. Results: On two-way analysis of variance with repeated measures on time factor, significant treatment and interaction effects on muscle endurance were found. A significant interaction effect, but not treatment effect, was found for shoulder pain. Post hoc test showed that the shoulder pain was reduced immediately after intervention (treated group) and 2weeks (control and treated group) after the intervention as compared to before the intervention. Conclusions: This study suggests that sacrooccipital category II blocking can be used to alleviate shoulder pain caused by pelvic instability. The mechanisms behind the long-term benefits may include an increase in abdominal muscle endurance.