Specific reference request for category theory

category-theoryreference-request

What are some textbook that contain material about monoidal categories and monoid objects? I have seen Awodey's and Riehl's books and they don't seem to cover this part, while Mac Lane is way too dense to be used for my course. I accept even other kind of sources, like sites or online lectures, but I have to exclude nLab because it uses higher category theory.

Best Answer

Here are some resources on monoidal categories (including monoid objects) which I found quite useful and detailed as a beginner:

  • P. Etingof, S. Gelaki, D. Nikshych, V. Ostrik. Tensor Categories, Mathematical Surveys and Monographs, Vol. 205. Link (Chapter 2)
  • N. Saavedra-Rivano. Categories Tannakiennes, Lectures Notes in Mathematics, Vol. 265, Springer, 1972. Link (Chapter 1)
  • F. Borceux. Handbook of Categorical Algebra: Volume 1, Basic Category Theory, volume 50 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1994. Link (Chapter 7)

Borceux "only" treats bicategories, but monoidal categories are just one-object bicategories, and general bicategories are not much more difficult to understand.

In case you know German, you can also check out my book which treats monoidal categories in depth.

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