Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Monoidal category. $\lambda_I = \rho_I : I\otimes I\to I$? If this equality can not be proved, in what categories it is false?

share|cite|improve this question

This condition follows from the other axioms. I suggest you take a look at a beautiful J. Kock's paper "Elementary remarks on units in monoidal categories", which describes monoidal categories from a bit different (and more coherent) perspective.

However, proving the condition "by hand" may be a good exercise for you.

share|cite|improve this answer
Thank you. To be honest, I failed to do this exercise without peeking, though tried with at least 1 page of diagrams. :) In Kock's paper there are words: “Shortly after, it was shown by Kelly [6] that one of these four axioms for units in fact implies the three others. His proof constitutes nowadays the first three lemmas in many treatments of monoidal categories…” Can you recommend some treatments of monoidal categories (not written by Kelly, please :) )? @Mockup: – beroal Jul 25 '11 at 0:21
For a good introductory text you may try the following: P. Selinger, "A survey of graphical languages for monoidal categories.". – Michal R. Przybylek Jul 25 '11 at 17:55

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.