There's a category Braid, or Brd, whose objects are the natural numbers and morphisms "n parallel pieces of string twisted around each other". And a related one Tng where the objects distinguish between 'string going in' and 'string going out', and strings are allowed to double back on themselves. Related to these two these is a category whose objects are again the natural numbers, and whose morphisms are pieces of string which are allowed to split into multiple strands, and join together into single strands, such as the following morphism 3 --> 2: * * * \ / / | /\ \ / | \/ | * * (excuse the crude drawing which will only look OK if you have a monospaced font). There are various ways this category could be formulated (are the strings allowed to cross each other? are they allowed to double back? etc), but my question is: has anything been written about it? Does it have a name? Does it remind anyone of another category which has been studied? Yours, Jules Bean 20-Sep-2001 20:06:37 -0300,6821;000000000001-0000001a