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Applications of categorical algebra. (Russian. English original) Zbl 0588.18009

Russ. Math. Surv. 40, No. 4, 73-80 (1985); translation from Usp. Mat. Nauk 40, No. 4 (244), 69-75 (1985).
This paper reviews the interaction of homotopy theory and category theory especially in the treatment of coherence phenomena. Brief descriptions are given of various apparently distinct ideas such as that of an indexed category, a crossed module and a multiple category and an outline is given of some of the complex interactions between these concepts. The quite extensive bibliography should be useful to anyone starting in this area.
Reviewer: T.Porter

MSC:

18G55 Nonabelian homotopical algebra (MSC2010)
55P99 Homotopy theory
18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
18D30 Fibered categories
20J05 Homological methods in group theory
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