Key questions: Normalization is a basic cortical computation through which the excitability of cortical neurons changes in a manner that is inversely proportional to the overall activity level of the network (Heeger, 1992). It can account for several properties of cortical sensory processing, ranging from cross orientation suppression in the visual system (Freeman et al., 2002), to the modulation of sensory responses with attention (Reynolds and Heeger, 2009). The potential involvement of inhibition in cortical normalization is debated (Katzner et al., 2011) and needs to be elucidated. Furthermore, while the role of inhibition in gain modulation, another basic cortical operation, is better established, the exact contribution of the various inhibitory circuits to this operation still needs to be assessed.