C. Ehresmann,Categories Structurees, Ann. Sci. Ecole Norm. Sup. 80 (1963), 349-425.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a double reflexive graph. Its cells are homotopy classes of colourings of certain rectangular complexes in the plane. A number of examples illustrate the wide variety of combinatorial properties of the plane this touches. 1 Introduction Double categories were introduced in 1963 by Ehresmann [3]. Since then, considerable work has been done, much of it in the context of homotopy theory (see XXX) Of course, a 2 category is a special kind of double category [8] so that all work done on 2 categories (and bicategories) is also saying something about double categories. In particular, the ....

C. Ehresmann,Categories Structurees, Ann. Sci. Ecole Norm. Sup. 80 (1963), 349-425.

....convenient but limited derivation with an elementary development of homology based on monoids instead of groups to yield what we feel will be a more comprehensive and convincing algebrization. To be more precise, we base it not exactly on monoids but rather on their generalization to n categories [Ehr63] following roughly the lines of Street [Str87] as more appropriately expressing the dimensional aspect. 7 Extensions of Event Structures Despite the fact that event structures were introduced more than a decade ago [Win80] there have been no further generalizations of event structures where ....

....properties of groups, to permit their easy adaptation to the irreversible case. We would be delighted to have a pointer to a counterexample. The following notion of higher dimensional automaton takes its inspiration not from algebraic topology but instead from the geometry of n categories [Ehr63]. Ordinarily we define an automaton as an edge labeled graph, and define its operation in terms of the paths in that graph and the operation of path concatenation. However we could just as well start with the paths and dispense with the underlying graph. When passing from discrete to continuous ....

C. Ehresmann. Categories structurees. Ann. Sci. Ecole Norm. Sup., 80:349--425, 1963.

....2 categories, where multiple compositions present complicated pasting problems, and from bicategories, where the basic laws (such as associativity, and the existence of identities) hold only up to equivalence. Double groupoids were introduced by Ehresmann in the early 1960 s (see for example [9], 7] but primarily as instances of double categories, and as a part of a general exploration of categories with structure. Since that time their main use has been in homotopy theory. Brown and Higgins [2] gave the earliest example of a higher homotopy groupoid , by associating to a pointed ....

C. Ehresmann. Cat'egories structur'ees. Ann. Sci. ' Ecole Norm. Sup. (3), 80:349--426, 1963. Contained in [8], Partie III-1.

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