nLab
IPC-property

Idea

The IPC-property (“inductive limit product commutation property”) is a technical condition on a category AA which ensures that presheaves with values in AA have a good notion of sheafification.

Definition

A category AA is said to satisfy the IPC-property if

the canonical morphism

colim( sI sk sα s(π s(j))A) scolimα s colim \left( \prod_s I_s \stackrel{k \mapsto \prod_s \alpha_s(\pi_s(j))}{\to} A \right) \to \prod_s colim \alpha_s

is an isomorphism.

References

The IPC property is definition 3.1.10 in

It is invoked for sheafification in section 17.4 there.

Created on March 31, 2009 19:06:54 by Urs Schreiber (134.100.222.156)