Localizations of Transfors

Let be n-dimensional teisi, i.e., higher-dimensional Gray-categorical structures. The following questions can be asked. Does a left q-transfor , i.e., a functor 2_q, induce a right q-transfor , i.e., a functor More generally, does a functor induce a functor For k-arrows c and whose (k – 1)-sources and targets agree, does a q-transfor induce a q-transfor , for appropriate k-arrows For k-arrows c and whose (k – 1)-sources and targets agree, does a q-transfor induce a (q + k + 1)-transfor , for appropriate k-arrows I give answers to these questions in the cases where n-dimensional teisi and their tensor product have been defined, i.e., for n 3, and for n up to 5 in some cases that do not need all data and axioms of n-dimensional teisi.I apply the above to compositions in teisi, in particular to braidings and syllepses. One of the results is that a braiding on a monoidal 2-category induces a pseudo-natural transformation , where is the reverse of ? –, which is almost, but not quite, equal to – ?. However, in higher dimensions need not be reversible, so a braiding on a higher-dimensional tas can not be seen as a transfor A B B A.