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Methods of calculating cohomological and Hochschild-Mitchell dimensions of finite partially ordered sets. (English) Zbl 0988.18009

Homology Homotopy Appl. 3, No. 1, 101-110 (2001).

B. Mitchell [Adv. Math. 8, 1-161 (1972; Zbl 0232.18009)] described finite partially sets of Hochschild dimension \(0\), \(1\) and \(2\). C. C. Cheng [J. Algebra 40, No. 2, 340-347 (1985; Zbl 0337.18008)] characterized such sets of cohomological dimension one.
The authors present algorithms for calculating those dimensions by means of elementary operations on rows of columns of some matrices with integral entries.

Reviewer: Marek Golasiński (Toruń)

MSC:

18G20	Homological dimension (category-theoretic aspects)
06A06	Partial orders, general

Keywords:

cohomological dimension; Hochschild dimension; cohomology of categories; partially ordered set

Citations:

Zbl 0232.18009; Zbl 0337.18008

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