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6

Note that taking opposite category gives rise to a $2$-endofunctor: $$(-)^{op}:\mathrm{CAT}\rightarrow \mathrm{CAT}$$ on $2$-category of all categories contained in a given universe $\mathcal{U}$. This $2$-endofunctor is covariant on functors and contraviariant on natural transfromations. Using this $2$-endofunctor you can argue as follows. If $$(\mathcal{C}...


0

The authors define: "A monoidal functor F is said to be an equivalence of monoidal categories if it is an equivalence of ordinary categories." I.e. a monoidal equivalence F is an equivalence, and F is equipped with a monoidal structure J. Since F is an equivalence, it admits a quasi-inverse G such that FG and GF are isomorphic to the respective identity ...



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