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Isn't the second definition wrong? Should it end in --ev(x)id_X*--> X* ? [(x)is meant to be tensor product]
Likewise, shouldn't the last morphism of the first definition be ev (x) id_Y ?
Is there a difference (other than the terminology) between this and the concept of a compact closed category? 137.122.30.238 (talk) 00:39, 15 December 2009 (UTC)
- Not that justifies a separate article from what I see. I wrote a summary of the unique parts of each to help with a merge. See it on the compact closed category talk page.Expz (talk) 13:44, 15 December 2009 (UTC)
Rigid symmetric monoidal categories date back (at least) to the following book, where they are explicitly defined under this name. They might already appear in the author's preceding papers.
Saavedra Rivano, Neantro: Catégories Tannakiennes. Lecture Notes in Mathematics, Vol. 265. Springer-Verlag, Berlin-New York, 1972. ii+418 pp. —Preceding unsigned comment added by 131.174.22.118 (talk) 15:19, 4 March 2010 (UTC)
A rigid category is a category in which each object has a dual object, so the two pages "Rigid Category" and "Dual Object" should be merged.
Also, the term "rigid" is used in algebraic geometry whereas "autonomous" is used in category theory. It would be nice to create and then redirect "Autonomous Category" to this page.