The analog of the notion of opposite category for (∞,1)-categories.
For an (∞,1)-category regard it in its incarnation as a ∞-groupoid-enriched category. Then its opposite is the -category with the same objects and with hom-objects given by
with the obvious composition law.
With incarnated as a quasi-category, the simplicial set is that obtained by reversing the order of all the face and degeneracy maps. See opposite quasi-category.
The operation extends to an automorphic (∞,1)-functor
from (∞,1)Cat to itself. Up to equivalence, this is the only nontrivial such automorphism. For more on this see (∞,1)Cat.
Revised on February 24, 2010 18:36:09
by Urs Schreiber