Preprint available: Close categories vs. closed multicategories
Dear category theorists, May I draw to your attention my paper "Close categories vs. closed multicategories" available at http://arxiv.org/abs/0904.3137 In the paper I prove that the 2-category of closed categories of Eilenberg and Kelly is equivalent to a suitable full 2-subcategory of the 2-category of closed multicategories. Comments are welcome! Best, Oleksandr -- "Dealing with failure is easy: Work hard to improve. Success is also easy to handle: You've solved the wrong problem. Work hard to improve." - Alan Perlis
Dear Vaughan,
Very interesting definition. Do you have an example of a closed category that cannot be expanded to a closed monoidal category? If there's one in your paper then my apologies for overlooking it.
Every closed category can be embedded fully faithfully into a closed monoidal category such that the closed structure is preserved; this is due to Laplaza (exact reference in my paper). However, non-monoidal closed categories do occur. I was motivated by the example of A-infinity categories, and frankly, I am not aware of any other non-trivial and non-artificial examples, but I am sure there must be some, it is just my ignorance. Best, Oleksandr -- "Dealing with failure is easy: Work hard to improve. Success is also easy to handle: You've solved the wrong problem. Work hard to improve." - Alan Perlis
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Oleksandr Manzyuk