I am sorry for posting this again, but I have received an empty message from the categories list. [Note from moderator: From the categories list web-page: "Do not send attachments, html or excessively long postings (greater than about 10K). Postings with attachments will be discarded; long postings or ones with html may be." The reason an empty message arrives is that the moderator sometimes inadvertently mishandles a message containing the header: "Content-Type: multipart/alternative; ..." This header is associated with html and messages sent in multiple formats. It is time-wasting to deal with such messages. For good reasons, categories is a *text* mailing list. For example, consider: http://pyropus.ca/personal/writings/nomime.html or http://home.earthlink.net/~bobbau/email/avoiding-html/ If you want your messages to be posted on categories, please ensure that you send only text-only posts. The URLs just quoted contain help to do this. Other messages *will* be discarded. Thanks. ] ---------- Forwarded message ---------- From: Tony Meman <tonymeman1@googlemail.com> Date: 2009/10/3 Subject: Terminology problem with monoidal adjunctions To: categories <categories@mta.ca> Dear mathematicians, I have a terminology problem concerning monoidal adjunctions and would therefore like to ask some experts. Let V and W be two symmetric monoidal categories and L: V <--> W :R an adjunction of (lax) symmetric monoidal functors, .i.e. the unit and the counit are monoidal natural transformations. In a previous post, it was pointed out to me that L have to be automatically a strong symmetric monoidal functor then (I do not remember if the monoidal structures have to be closed for this implication). I have read the term 'strong symmetric monoidal adjunction' and it seems to me that this is just a monoidal adjunction with a strong monoidal L. Why is this definition not redundant? I have also read about a 'strict symmetric mnonoidal adjunction'. This confuses me totally, since I have the impression that there is sometimes inconsistency in the use of the term 'strict' and 'strong'. Thank you for any help. Tony [For admin and other information see: http://www.mta.ca/~cat-dist/ ]