Massol, A. Minimality of the system of seven equations for the category of finite sets. (English) Zbl 0903.18001 Theor. Comput. Sci. 176, No. 1-2, 347-353 (1997). Summary: A. Burroni [Theor. Comput. Sci. 115, No. 1, 43-62 (1993; Zbl 0791.08004)], and later Y. Lafont [Lond. Math. Soc. Lect. Note Ser. 177, 191-201 (1992; Zbl 0789.18004)], proposed a presentation of the monoidal category of finite sets with three generators and seven equations. We prove that none of these equations is superfluous by considering interpretations into monoidal categories. Cited in 3 Documents MSC: 18B05 Categories of sets, characterizations 68Q42 Grammars and rewriting systems 68Q70 Algebraic theory of languages and automata 18D10 Monoidal, symmetric monoidal and braided categories (MSC2010) 18C10 Theories (e.g., algebraic theories), structure, and semantics 18B20 Categories of machines, automata Keywords:rewriting systems; algebraic theories; word problems; monoidal category of finite sets Citations:Zbl 0791.08004; Zbl 0789.18004 PDFBibTeX XMLCite \textit{A. Massol}, Theor. Comput. Sci. 176, No. 1--2, 347--353 (1997; Zbl 0903.18001) Full Text: DOI References: [1] Burroni, A., Higher dimensional word problem, Theoret. Comput. Sci., 115, 43-62 (1993) · Zbl 0791.08004 [2] Lafont, Y., Penrose diagrams and 2-dimensional rewriting, (Fourman, M. P.; Johnstone, P. T.; Pitts, A. M., Applications of Categories in Computer Science. Applications of Categories in Computer Science, LMSLNS, Vol. 177 (1992), Cambridge Univ. Press: Cambridge Univ. Press Cambridge), 191-201 · Zbl 0789.18004 [3] Lafont, Y., Equational reasoning with 2-dimensional diagrams, (Lecture Notes in Computer Science, Vol. 909 (1995), Springer: Springer Berlin), 170-195 [4] Mac Lane, S., Categories for the Working Mathematician, (GTM, 5 (1971), Springer: Springer Berlin) · Zbl 0906.18001 [5] Penrose, R.; Rindler, W., Spinors and Space-time, Vol. 1: Two-spinor Calculus and Relativistic Fields (1986), Cambridge Univ. Press: Cambridge Univ. Press Cambridge · Zbl 0602.53001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.