Hi, then , in this setting, how coherence should be interpreted? According to Mac Lane, a coherence theorem asserts commutativity of a class of diagrams; some other authors mean rather decision procedure/criteria for commutativity of diagrams. By the way, did you consider some kind of "basic" arrows and generated "canonical maps"? Do there appear/be used some known types of categories with structure (cartesian, monoidal, cartesian closed, monoidal closed)? Another interesting question could be isomorphism of objects. Best wishes Sergei Soloviev Hi all,
The basic idea of my talk was this: one can think of any category C as a "database schema": the objects of C are called "tables" and an arrow f:A-->B is called a "column of table A with values in table B". Now a functor C-->Sets is a "state" of that database: it fills every table with a set of rows. Leaf objects of C (objects with no outgoing arrows) correspond to "pure data." One can thus visualize a category as a system of tables; commutative diagrams correspond to "rules" such as "the secretary of a department must be in that department."
Using sketches instead of categories allows a little more flexibility, but the basic idea is as above. The model is nice for a variety of reasons, most of all its simplicity. In polite contradiction to one of Diskin's claims, two database administrators (at two large multi-national corporations) that I know think it is a viable model. They do not balk at the idea of data columns being considered as foreign keys. It puts everything on the same playing field.
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