A class of objects in a cartesian closed category is called an exponential ideal if whenever and , the exponential object is in .
Of course, in particular this implies that is itself cartesian closed.
This appears for instance as (Johnstone, A4.3.1).
The relation of exponential ideals to reflective subcategories is discussed in section A4.3.1 of
Revised on November 14, 2011 21:15:39
by Urs Schreiber