fully faithful (infinity,1)-functor
The generalization to the context of (∞,1)-category-theory of the notion of a full and faithful functor in ordinary category theory.
An (∞,1)-functor is full and faithful if for all objects it induced an equivalence on the hom-∞-groupoids
A full and faithful -functor exhibits as a full sub-(∞,1)-category of and one tends to write
to indicate this.
A full and faithful -functor is precisely a monomorphism in (∞,1)Cat, hence a (-1)-truncated morphism.
An (∞,1)-functor which is both full and faithful as well as an essentially surjective (∞,1)-functor is an equivalence of (∞,1)-categories.
This appears as definition 1.2.10 in
Revised on May 12, 2012 04:07:28
by Mike Shulman