Abstract:
We construct various multiple categories, based on generalised Ehresmann
quintets. The main construction is a multiple category whose objects are all
the 'lax' multiple categories; the transversal arrows are their strict
multiple functors while the arrows in a positive direction are 'multiple
functors of a mixed laxity', varying from the lax ones (in direction 1) to the
colax ones (in direction ∞).
Keywords:
multiple category, double category, cubical set, quintet.
MSC:
18
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