Preprint available: Close categories vs. closed multicategories

Preprint available: Close categories vs. closed multicategories

[Oleksandr Manzyuk]

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

Re: Preprint available: Close categories vs. closed multicategories

[Oleksandr Manzyuk]

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