Talk:Autonomous category

From Wikipedia, the free encyclopedia

"In mathematics, an autonomous category is another term for a symmetric monoidal closed category."

This is not current usage. An autonomous category is a monoidal category in which every object has a left and a right dual. A left autonomous category is a monoidal category in which every object has a left dual, etc.

Autonomous category is synonymous with compact category or rigid category. Some people use compact to mean symmetric autonomous category.

An autonomous category is a closed category. The internal hom of A and B is .

The principal example of an autonomous category is the category of vector spaces (over k) with A* given by the dual of A, Hom(A,k).

Are you sure you are not confusing with *-autonomous categories ?

Yes, I am sure that I am not. But, indeed, I made a mistake in the line above. What I meant to say is that the principal example of an autonomous category is the category of finite-dimensional vector spaces. For *-autonomous categories the principal example is topological vector spaces, possibly infinite dimensional. The dualising object is of course given by the underlying field k.

Lkajdf 12:20, 16 June 2007 (UTC)