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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

• CommentRowNumber1.
• CommentAuthorMike Shulman
• CommentTimeJan 6th 2010

I created cograph of a profunctor and added some references to it at cograph of a functor. All the cograph pages could probably use some unifying work.

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeJan 6th 2010

Often called the collage of a bimodule/profunctor?

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeJan 6th 2010

Or sometimes, at least. Is that very common? I recall one paper of Street's that uses "collage" to mean "lax colimit". I've never been clear what the advantage is of a new word (whose meaning you have to remember) over "lax colimit."

• CommentRowNumber4.
• CommentAuthorUrs
• CommentTimeJan 7th 2010
• (edited Apr 29th 2010)

I prefer "cograph" as "graph" is nicely descriptive and standard, and "cograph" the evident dualization.

If "collage" is what other people use I'd be in favor of saying so prominently at the beginning of the entry, but leave the entry title as "cograph". I think the fact that there is a notion of "cograph" is quite pleasing.

• CommentRowNumber5.
• CommentAuthorTodd_Trimble
• CommentTimeJan 7th 2010

I agree that "cograph" is a better name for it, but I did hear "collage" a certain amount when I was in Australia [from Street and Verity, maybe Kelly too], and I thought I had also seen it used by Johnstone and Carboni (in their paper on Artin gluing and parametric representability) but maybe my memory deceives me here. I agree with Urs that the usage should be noted.

• CommentRowNumber6.
• CommentAuthorUrs
• CommentTimeApr 29th 2010

added to cograph of a profunctor details on the $(\infty,1)$-categorical case and linked to inner fibration.