# Reading about monoidal functors

Can anybody recommend me a textbook about monoidal functors? I need elementary facts about them for references, for example, that a monoidal functor turns every monoid into a monoid. Thank you in advance.

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## 1 Answer

• N. Saavedra-Rivano, Catégories Tannakiennes, Lectures Notes in Mathematics, Vol. 265, Springer-Verlag, 1972.
• M. Kashiwara, P. Shapira, Categories and Sheaves, Grundlehren der mathematischen Wissenschaften 332, Springer-Verlag, 2005.
• P. Etingof, S. Gelaki, D. Nikshych, V. Ostrik, 18.769 Topics in Lie Theory: Tensor Categories, lecture notes online
• S. Mac Lane, Categories for the working mathematician, Graduate Texts in Mathematics 5, Springer-Verlag, 1971.
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Martin, where do they mention this fact (that a monoid is turned into a monoid)? –  Sergei Akbarov Nov 3 '13 at 21:14
Please, do this yourself. These are four excellent resources for monoidal categories, and I am sure that they contain this (trivial) fact. –  Martin Brandenburg Nov 3 '13 at 22:21
It's worth pointing out that the second edition of CWM has a whole extra chapter on symmetric/braided monoidal categories. –  Zhen Lin Nov 4 '13 at 0:22
Martin, look at this: search.rsl.ru/ru and libserv.mi.ras.ru/book.asp. These are two main libraries for mathematicians in Moscow (the Russian State Library, and the library of the Mathematical Institute). They don't contain the first two books in your list. The third and the fourth books are available (the 3rd is in the net and the 4th was published in Russian), but they don't contain this result. That was actually why I asked this question. –  Sergei Akbarov Nov 4 '13 at 3:07
@SergeiAkbarov these are books you were looking for: 1, 2 –  no identity May 25 at 23:16