The nucleophilic carbon atom of the ylide reacts with the Michael group first and in the second step the electrophilic part is displaced as the leaving group with ring closure. A chiral moiety can then interact or is part of either with the carbonyl group (amine organocatalysis) or with the leaving group. Pioneering work originates from Johnson & Schroeck using a oxosulfonium methylide (1968 DOI) and from Trost & Hammen (sulfonium ylide, 1973 DOI). Phosphonium ylide MIRC reactions exist since 1988 (Krief et al. DOI)
First of is Aggarwal whose group in 2001 building on asymmetric epoxidations and aziridations ( DOI) invented an complex indirect sulfonium ylide method (DOI).