C -> D,
induce a right q-transfor C -> D, i.e., a functor
C 2q -> D?
More generally, does a functor C
D -> E
induce a functor
D C -> E?
For k-arrows c and c'
C
whose (k-1)-sources and targets
agree, does a q-transfor C -> D induce a q-transfor
C (c,c') -> D (d,d'), for appropriate k-arrows d and d'
D?
For k-arrows c and c'
C
and d and d'
D whose
(k-1)-sources and targets agree, does a q-transfor
C D -> E induce a
(q+k+1)-transfor
C (c,c') D (d,d') ->
E (e,e'), for appropriate k-arrows e and e'
E?
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
? -,
whichis 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.
``The author acknowledges the support of the
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