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Published in:
2005 | OriginalPaper | Chapter
Abstract Scalars, Loops, and Free Traced and Strongly Compact Closed Categories
Author : Samson Abramsky
Published in: Algebra and Coalgebra in Computer Science
Publisher: Springer Berlin Heidelberg
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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 variations where a prescribed monoid of scalars can be ‘glued in’ to the free construction.