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• CommentRowNumber1.
• CommentAuthorPeter Heinig
• CommentTimeJul 3rd 2017

Added a literature reference to icon. Started some systematic notes on icons for monoidal-enriched bicategories, which I am currently using for something. Think the broken-off state of that section is not intolerable, in particular since I have seen similar work in progress on the nLab. Intend to continue them soon.

• CommentRowNumber2.
• CommentAuthorMike Shulman
• CommentTimeJul 4th 2017

I don’t think that this is the place to recall the definition of enriched functor of bicategories.

• CommentRowNumber3.
• CommentAuthorPeter Heinig
• CommentTimeJul 4th 2017

I don’t think that this is the place to recall the definition of enriched functor of bicategories.

Removed it.

Is there a place on the nLab where an exposition of parts of, and material related to, the article Adv. Math. 289, 1–94, would fit? (There are detailed expository parts of the nLab; for bicategories and string diagrams there appear not to be detailed nLab expositions yet.)

• CommentRowNumber4.
• CommentAuthorMike Shulman
• CommentTimeJul 5th 2017

Well, there’s room for quite a lot more at enriched bicategory. The definition of enriched icon could certainly go at icon. If you want to write a lot about functors, it could go on a new page like enriched pseudofunctor. A small amount about the relevant kind of limits could be included at 2-limit, or if you want to write a lot then maybe it would be worth having its own page like enriched 2-limit or something. If you want to write about the tricategory of enriched modules, you could maybe create 2-profunctor. (On the nLab I believe the usual convention is still that, contrary to much of the literature, the prefix “2-” doesn’t imply strictness, only 2-dimensionality, thereby avoiding the need for words like “bilimit”.) The second half of the paper could maybe go at profunctor or proarrow equipment, or perhaps we could go for the new naming-pages-after-theorems convention and make enriched categories, functors, and profunctors are a free cocompletion. There are other possibilities as well.

• CommentRowNumber5.
• CommentAuthorPeter Heinig
• CommentTimeJul 5th 2017
• (edited Jul 5th 2017)

Especially with

(On the nLab I believe the usual convention is still that, contrary to much of the literature, the prefix “2-” doesn’t imply strictness, only 2-dimensionality, thereby avoiding the need for words like “bilimit”.)

you preempted a question of mine (I had taken care to use the “bi”-prefix in the planned page on icons, since the plan was and is to better learn and document the constructions for weak 2-categories, and then was surprised that the usage was edited back to the “2-” convention).

• CommentRowNumber6.
• CommentAuthorvarkor
• CommentTimeMar 9th 2023

Briefly mention relation to double categories.