nLab
faithful morphism

Definition

A morphism f:ABf\colon A\to B in a 2-category KK is said to be (representably) faithful if for all objects XX, the induced functor

K(X,A)K(X,B)K(X,A) \to K(X,B)

is faithful. In Cat, this is equivalent to ff being faithful in the usual sense.

Remarks

Revised on May 21, 2010 19:14:45 by Mike Shulman (128.192.37.11)