Various approaches to products of residue currents

We describe various approaches to Coleff–Herrera products of residue currents Rj (of Cauchy–Fantappiè–Leray type) associated to holomorphic mappings fj. More precisely, we study to which extent (exterior) products of natural regularizations of the individual currents Rj yield regularizations of the corresponding Coleff–Herrera products. Our results hold globally on an arbitrary pure-dimensional complex space.