Some remarks on the subject of coherence. (English) Zbl 0358.18008

Voreadou, Rodiani

Cah. Topol. Géom. Différ. 15, 399-417 (1974).

The author has published now, in the Mem. Am. Math. Soc. 182 (1977; Zbl 0347.18008) a final treatment of coherence problems in closed categories. The present paper is a preliminary version which already contains the main ideas. In a first part of the paper, the author describes a class \(\mathfrak M\) of graphs and proves that, for allowable natural transformations \(h\) and \(h'\), \(h = h'\) is equivalent to \((h,h')\notin \mathfrak M\). The end of the paper contains some first remarks on non commutative diagrams.

Reviewer: Francis Borceux (Louvain-La-Neuve)

MSC:

18D15

Closed categories (closed monoidal and Cartesian closed categories, etc.)

Citations:

Zbl 0347.18008

References:

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[3]	G.M. Kelly and S. Maclane , Coherence in Closed Categories , J. Pure and Applied Algebra 1 ( 1971 ), 97 - 140 . MR 283045 | Zbl 0212.35001 · Zbl 0212.35001
[4]	G.M. Kelly and S. Maclane , Closed Coherence for a Natural Tiansformation , Lecture Notes in Math. 281 , Springer ( 1972 ), 1 - 28 . MR 374237 | Zbl 0245.18003 · Zbl 0245.18003
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[6]	R. Voreadou , A Coherence Theorem for Closed Categories, Ph. D. Thesis , The University of Chicago , 1972 . · Zbl 0347.18008
[7]	R. Voreadou , Non-commutative diagrams in closed categories ( to appear) . · Zbl 0347.18008