MSGSS
Talk by Scott Wesley
Algebraic presentations allow us to study mathematical objects through their generators and the relations those generators satisfy. In this talk, we will begin by reviewing monoid presentations and seeing how this generalizes to PROP categories. Since free PROP categories can be understood as collections of circuit diagrams, then this formalism is ideal for studying circuits and their compositional properties. This approach has proven particularly successful in the context of quantum computing. However, this approach struggles with characterizing conditional statements, which are essential in all models of computation. In this talk, we will look at some preliminary results on identifying conditional structures in PROP categories, and challenges that arise when freely generating these conditional structures.