The process whose specific outcome is the progression of a cerebral cortex GABAergic interneuron over time, from initial commitment to its fate, to the fully functional differentiated cell. [ http://purl.obolibrary.org/obo/go/references/0000021 GOC:dgh GOC:dph http://www.ncbi.nlm.nih.gov/pubmed/12626695 GOC:jid GOC:cls ]