We address the connection between conceptual knowledge and cognitive control using a neural network model. This model extends a widely held theory of cognitive control [Cohen, J. D., Dunbar, K., & McClelland, J. L. On the control of automatic processes: A parallel distributed processing model of the Stroop effect. Psychological Review, 97, 332-361, 1990] so that it can explain new empirical findings. Leveraging other computational modeling work, we hypothesize that representations used for task control are recruited from preexisting representations for categories, such as the concept of color relevant to the Stroop task we model here. This hypothesis allows the model to account for otherwise puzzling fMRI results, such as increased activity in brain regions processing to-be-ignored information. In addition, biologically motivated changes in the model's pattern of connectivity show how global competition can arise when inhibition is strictly local, as it seems to be in the cortex. We also discuss the potential for this theory to unify models of task control with other forms of attention.