Gromov initiated what he calls “symbolic algebraic geometry”, in which he studied proalgebraic varieties. In this paper we formulate a general theory of characteristic classes of proalgebraic varieties as a natural transformation, which is a natural extension of the well-studied theories of characteristic classes of singular varieties. Fulton–MacPherson bivariant theory is a key tool for our formulation and our approach naturally leads us to the notion of motivic measure and also its generalization.
"Characteristic classes of proalgebraic varieties and motivic measures." Algebr. Geom. Topol. 12 (1) 601 - 641, 2012. https://doi.org/10.2140/agt.2012.12.601