Download Category Theory and Computer Science: 7th International by John C. Baez (auth.), Eugenio Moggi, Giuseppe Rosolini PDF

By John C. Baez (auth.), Eugenio Moggi, Giuseppe Rosolini (eds.)

This e-book constitutes the refereed complaints of the seventh foreign convention on type thought and machine technology, CTCS'97, held in Santa Margheria Ligure, Italy, in September 1997.
Category conception draws curiosity within the theoretical laptop technological know-how group as a result of its skill to set up connections among assorted parts in desktop technology and arithmetic and to supply a couple of widely used rules for organizing mathematical theories. This publication provides a variety of 15 revised complete papers including 3 invited contributions. the themes addressed comprise reasoning rules for forms, rewriting, software semantics, and structuring of logical systems.

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Extra info for Category Theory and Computer Science: 7th International Conference, CTCS '97 Santa Margherita Ligure Italy, September 4–6, 1997 Proceedings

Sample text

An allegory A has three sub categories of special interest, the categories formed by taking just: (1) the simple arrows, also called partial functions; (2) the entire arrows, also called total relations; (3) the arrows that are both simple and entire, that is, functions. The subcategory of simple and entire arrows of an allegory A is denoted by Fun(A). For simplicity, the arrows of an allegory will be called relations, and the arrows of Fun(A) will be called functions. Allegories are very general, and extra conditions have to be imposed to get closer to set-theoretic relations.

Ak are the infaces of x and a' is the outface of x; all these are cells of one lower dimension. ,ak) ? ' aI is called a 'frame'. ,ak) ? , ? ,ak) ? " ? If one of these configurations (frame, niche, or punctured niche) can be extended to an actual cell, the cell is called an 'occupant' of the configuration. Occupants of the same frame are called 'frame-competitors', while occupants of the same niche are called 'niche-competitors'. 4 Universality The only thing we need now to define the notion of weak n-category is the concept of a 'universal' occupant of a niche.

There are some touchy points here worth mentioning. First, there is considerable freedom of choice involved in constructing the two (n + 1)-categories1 in question; one should do it in a 'reasonable' way, but this is not necessarily easy. Secondly, there is no guarantee that we might not get a different answer for the question if we reversed the roles of the two definitions. Nonetheless, it should be interesting to compare different definitions of weak n-category in this way. 31 A second solution is suggested by homotopy theory~ which again comes to the rescue.

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