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Patrick Nicodemus (Jun 10 2025 at 21:26):Hi, I need some constructive advice.
For a project I am working on, I needed to prove that, if is a 2-category and is an object in , then the lax slice 2-category has limits of some shape if has limits of shape , the slice categories have limits of shape , and these limits are appropriately preserved by the reindexing functors associated to 1-cells .
Then I figured, this seems to be more a result about 2-fibrations in general.
Then I figured, why not prove it about fibrations between bicategories, and not just fibrations?
So, I worked out an appropriate limit lifting theorem for bicategories that generalizes the usual limit lifting theorem for Grothendieck fibrations. This is about a 10-12 page research note.
I don't really know what to do with it. I could upload it to the Arxiv to start with but I'm wondering if it's worth publishing. On one hand I feel that translating results from 1- and 2-category theory into bicategory theory could be seen as a mundane and tedious exercise in checking coherence conditions. On the other hand if somebody else needs this result, I have already done said mundane tedious work of proving it for them.
What should I do with this? Is it worth publishing in your opinion? I have not published before in mathematics.
John Baez (Jun 10 2025 at 22:02):At the very least you should put it on the arXiv, so people can easily find it and use its results and cite it. This will help the world and even help you a bit.
John Baez (Jun 10 2025 at 22:07):As for whether it's publishable, if it's a solid useful result and you feel you've proved it efficiently and written a clear, readable paper about it, I'd lean toward submitting it for publication and seeing what the referees think.