A Quantum Groups Primer by Shahn Majid

V between categories specifies an object F(V) E V for every object V E C, and a morphism F(4) : F(V) -+ F(W) for every morphism 0 : V , W, such that F(q o 0) = F(¢) o F(,) for F(W) -F(V) and F(q o 0) = F(O) o F(¢). morphisms. A `contravariant functor' is similar but with Less obvious is the notion of a natural transformation 9 : F --* G or 0 E Nat(F, G) between two functors F, G : C -* V.

Similarly for IF-1 with inverse braid crossings.

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