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.

本文研究了量子力学范畴公理化研究中近期作者和 Bob Coecke 提出的结构，特别是强紧闭范畴的概念。我们解释了如何利用这些结构来支持标量概念，并展示了强紧闭概念是经典的紧闭范畴概念的明显改进。之后，我们进一步讨论了一系列越来越复杂的结构化范畴的免费构造。