Non Symmetric Case
In a biclosed monoidal category C, not necessarily symmetric, it is still possible to define a dualizing object and then define a *-autonomous category as a biclosed monoidal category with a dualizing object. They are equivalent definitions, as in the symmetric case.
Read more about this topic: *-autonomous Category
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“One thing in any case is certain: man is neither the oldest nor the most constant problem that has been posed for human knowledge.”
—Michel Foucault (1926–1984)