preprint: Filtered colimits in the effective topos

preprint: Filtered colimits in the effective topos

[jvoosten]

A 7-page paper entitled

Filtered colimits in the effective topos

can be downloaded from:

http://www.math.uu.nl/people/jvoosten/effcolim.ps.gz

Abstract: we are concerned with the problem whether there
is a small full dense subcategory in the effective topos
(which would give a nice embedding of Eff into a sheaf
topos).
Since this topos has enough projectives, we may assume that
such a category consists of the \lambda-small projectives
for some cardinal \lambda.
Basically, there are two theorems:
1. For \lambda regular, uncountable: the \lambda -small
   projectives are dense, precisely if the constant objects
   functor \nabla :Sets --> Eff preserves
   \lambda-filtered colimits.
2. \nabla : Sets --> Eff does not preserve \omega _1-filtered
   colimits (hence, by 1., the countable projectives are
   not dense).

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