category theory application to database implementation
Hello CT community, Perhaps my question is too much of an applied question. I found a Web site where they say the following: "The category theory may become the core part of the mathematical instrument for the conceptual systems development. The system can be presented as a category in which the relative correlation exists among the objects (morphisms). Each system must be presented both on generalized and concrete reflection levels. The generalized level (upper level) and each of the concrete reflection levels are categories. Hence, it should be considered the process of reflection between general and concrete levels (functors). Each objects of the category system can be a system by itself (category). Consequently we have to consider lattice dependence of categories both on the generalized level and as well as on the decomposition of the objects. Each system changes in time. So it should be considered problems related to the dynamics of categories. Complex consideration and decisions of the above-stated and other related problems should ensure the formation of the mathematical base. This will enable to consider the creation of dynamic, unified distributed databases that can be used in various applied fields." What is this trying to say? Regards, Bill Halchin --------------------------------- Do you Yahoo!? Yahoo! News - Today's headlines --0-1797606253-1031952773=3D:84530 Content-Type: text/html; charset=3Dus-ascii <P>Hello CT community,</P> <P> Perhaps my question is too much of an applied q= uestion. I found a Web site where they say the following:</P> <P><FONT color=3D#000066>"The category theory may become the core part of t= he mathematical instrument for the conceptual systems development. The syst= em can be presented as acategory in which the relative correlation exists a= mong the objects (morphisms).<BR></FONT><FONT color=3D#000066 size=3D2>Each= system must be presented both on generalized and concrete reflection level= s. The generalized level (upper level) and each of the concrete reflection = levels are categories. Hence, it should be considered the process of reflec= tion between general and concrete levels (functors).<BR></FONT><FONT color= =3D#000066 size=3D2>Each objects of the category system can be a system by = itself (category). Consequently we have to consider lattice dependence of c= ategories both on the generalized level and as well as on the decomposition= of the objects.<BR></FONT><FONT color=3D#000066 size=3D2>Each system chang= es in time. So it should be considered problems related to the dynamics of = categories.<BR></FONT><FONT color=3D#000066 size=3D2>Complex consideration = and decisions of the above-stated and other related problems should ensure = the formation of the mathematical base. This will enable to consider the cr= eation of dynamic, unified distributed databases that can be used in variou= s applied fields." <BR></FONT></P> <P><FONT color=3D#000066 size=3D2>What is this trying to say?</P></FONT> <P><FONT color=3D#000066 size=3D2>Regards, Bill Halchin</P></FONT> <P><FONT color=3D#000066 size=3D2> </P></FONT><p><br><hr size=3D1>Do y= ou Yahoo!?<br> <b><a href=3D"http://news.yahoo.com/">Yahoo! News</a></b> - Today's headlin= es --0-1797606253-1031952773=3D:84530-- 18-Sep-2002 08:37:05 -0300,3366;000000000000-00000000
Bill Galchin's question concerns the appearance of category theory in a web page proposing to revamp the Georgian legislature (country of Georgia, not the US state), at http://www.asrios.ge/maincentreprojectsoverview_800.htm#reserch The proposal is in four sections. 1. Formation and Management of the Informational Legislative Space of Georgia. Six goals, ten tasks. General idea: formalize the legislature to the point where software methodology can support it. 2. A Theoretical Approach to the Formation of Progressive State Administration Structures Six objects, seven goals. General drift: update the administration. 3. Research on the Formation of Unified Dynamic Database Structure Based on Mathematical Models Idea: base the approach on categorial analysis, Petri nets, lattice theory, etc. (This is where the quote in question appeared.) 4. Training System "Increasing Efficiency of Organizations" Twelve training courses, five goals, four classes of personnel (administrators, captains of government and industry, entrepreneur-technologists, and students/trainees). The number of people likely to be fluent in both Georgian and category theory is presumably small enough to justify qualifying "stages" with "preliminary" in the proposal's conclusion: "Projects both theoretical and practical are at various stages of study." Vaughan Pratt 16-Sep-2002 17:27:06 -0300,3883;000000000000-00000000
The idea of a national government based on purely categorical principles is an interesting one. Suppose it had been tried elsewhere... "We hold these axioms to be the correct foundations, that all objects of the category M are isomorphic, that there is a functor from C creating certain equalizers... " -Robert Dawson 18-Sep-2002 15:53:14 -0300,3677;000000000000-00000000
participants (3)
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Galchin Vasili -
Robert J. MacG. Dawson -
Vaughan Pratt