  Here, we present a subcategory pEff of Hyland's Effective Topos Eff which can
be considered a predicative variant of Eff itself. The construction of pEff is
motivated by the desire of providing a "predicative" categorical universe of
realizers to model the Minimalist Foundation for constructive mathematics which
was ideated by the first author with G. Sambin in 2005 and completed into a
two-level formal system by the first author in 2009. pEff is a "predicative"
categorical universe because its objects and morphisms can be formalized in
Feferman's predicative weak theory of inductive definitions ID1^. Moreover, it
is a predicative variant of the Effective Topos for the following reasons.
First, pEff is a list-arithmetic locally cartesian closed pretopos of definable
objects in dID1 with a fibred category of small objects over pEff and a
(non-small) classifier of small subobjects. Second, it happens to coincide with
the exact completion on the lex category defined as a predicative rendering in
ID1^ of the subcategory of Eff of recursive definitions. As a consequence it
validates the Formal Church's thesis and it embeds in Eff by preserving the
list-arithmetic locally cartesian closed pretopos structure.
