Heriot-Watt Mathematics Report Series
HWM99-3, 21 Jan 1999
The convolution algebra of a matched category
N D Gilbert
Abstract
We discuss the structure of the flow monoid and the convolution
algebra of a category with a matched pair} of subcategories.
Matched pairs arise in the following way. Suppose that a category $\C$
possesses two subcategories $\H$ and $\V$ with the same set of objects as
$\C$, such that every arrow $\alpha \in \C$ may be written uniquely as
a composition $\alpha = \beta \circ \gamma$ with $\beta \in \H$ and
$\gamma \in \V$. We say that $\H$ and $\V$ are matched subcategories.
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