Abstract Scalars, Loops, and Free Traced and Strongly Compact Closed Categories

Scalars, Loops, and Free Traced and Strongly Compact Closed Categories Samson Abramsky Oxford University Computing Laboratory Wolfson Building, Parks Road, Oxford OX1 3QD, U.K. http://web.comlab.ox.ac.uk/oucl/work/samson.abramsky/ We study structures which have arisen in recent work by the present author and Bob Coecke on a categorical axiomatics for Quantum Mechanics; in particular, the notion of strongly compact closed category. We explain how these structures support a notion of scalar which allows quantitative aspects of physical theory to be expressed, and how the notion of strong compact closure emerges as a significant refinement of the more classical notion of compact closed category. We then proceed to an extended discussion of free constructions for a sequence of progressively more complex kinds of structured category, culminating in the strongly compact closed case. The simple geometric and combinatorial ideas underlying these constructions are emphasized. We also discuss ...

• Type: Conference
• Year: 2005
• Where: CALCO
• Authors: Samson Abramsky
• Keywords: CALCO 2005, Compact Closed Categories, Compact Closed Category, Strongly Compact Closed Category