Abstract
Compact closed categories have been exploited to provide compositional semantics for a variety of fields, including quantum computation and natural language processing. More recently, efforts have been made to apply these techniques to more unusual fields, such as the mathematical modelling of cognitive processes.
When applying these compositional techniques to a new field of investigation, the question often arises as to how to identify a suitable compact closed category capturing the phenomena of interest. The category of relations is a well known compact closed category and the notion of binary relation permits several different axes of variation. In this talk we will show how this freedom has been exploited in recent work to construct compact closed categories with a variety of desirable properties, and the general techniques that can be applied.