A NOTE ON THE RIGIDITY OF BRAIDED TENSOR CATEGORIES

Sara Pinter, Virgınia Rodrigues

Abstract


Given a monoidal (or tensor) category (C,⊗,I,a,l,r) dual objects of
an object are fundamental to define a rigid category. According to [5]
a monoidal categoryCis said to be left (right) autonomous when every
object has a left (right) dual object and it is autonomous or rigid if any
object has a left and a right dual object. In ([5], Proposition 7.2), the
authors proved that every left autonomous braided monoidal category is
autonomous. In this work we give another proof of this result showing
that for any braided category if an object has left dual object it also
has right dual, and conversely. We finalize with examples that show
the non-reciprocity of the concepts of monoidal, braided and symmetric
categories.


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