I'm reading about monoidal functors following the book "Tensor Categories" by Etingof. I'm really new to this topic so I've been struggle with the definitions and properties about monoidal categories and functors in general. I'm trying to prove Proposition 2.4.3 on page 31 in the following link (http://www-math.mit.edu/~etingof/egnobookfinal.pdf) but I simply don't know where to start. I would really appreciate if you can give me any hint to prove it myself. Thanks in advance.
Very simple question about monoidal functors
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$\begingroup$
category-theory
monoidal-categories
1 Answers
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Take the diagram (2.24) on page 30 and tensor it from right(left) with $F(X)$. Then use the natural morphism $J$ to show the first(second) diagram in proposition 2.4.3..