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Results tagged with higher-category-theory
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user 4262
For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
1
vote
Are fibrations coreflective in a 2-category?
Sketch of an answer: Remember that $E/e$ is equivalent to $\operatorname{Span} E(e,1) $, and that the (lax-idempotent) 2-monad whose algebras are fibrations is given by composition with the span $\Phi …
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2
votes
Accepted
Lax universality for lax limits
Adjunctions 'up to adjointness' have been considered before. Marta Bunge (Coherent extensions and relational algebras, Trans. AMS 197, 1974) called them 'lax adjunctions', John Gray (Formal category …
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5
votes
Accepted
Can we exhibit the 2-category of Grothendieck fibrations as a 2 (or 3)-limit?
I'm not sure whether you're working in Cat or 2-Cat; I'll assume the latter.
If B is an object of a finitely (2-)complete 2-category K, then the 2-category Fib(B) of fibrations over B is monadic over …
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3
votes
1
answer
371
views
Comparing discrete fibrations and their duals
I'm not sure if this is the right place to ask this question, but I'll ask it anyway, in the hope that some kindly Australian (true or honorary) is passing by and takes pity on me...
In Fibrations in …
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4
votes
Kan extensions of pseudofunctors
I haven't seen this written down anywhere, but I've worked it out myself in a paper I'm working on. The paper isn't quite ready, so I'll just sketch the idea here.
As Zhen says, you need to generali …
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4
votes
Accepted
Category enriched over a monoidal 2-category
Yes, here: R. Garner, M. Shulman, Enriched categories as a free cocompletion. arxiv.
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5
votes
Categorification of coends and ends
I don't think I have seen anything like this published before, but I have written up a similar definition here (see here too).
One thing in your definition I would take issue with is that your 2-coen …
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2
votes
Reference Request: Lax Ends
This page says that you may be able to get a copy by emailing Andrée Ehresmann.
I don't know the exact answer to your question, but if you can't find a reference then it may be worth recalling that:
…
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7
votes
Accepted
2-completeness analog of completeness theorem
Your suspicion is correct: in general, a V-category has all weighted V-limits if it has all conical V-limits and is cotensored over V (see Kelly's Basic Concepts of Enriched Category Theory, section 3 …
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5
votes
Accepted
Automorphisms and Bicategories
I don't see bicategories coming into this in a useful way, but I think what you have is a consequence of two more general facts:
The non-uniqueness of algebraic closures is a general fact about inje …
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6
votes
Is there a tricategory of bicategories and biprofunctors?
If you're still interested, I've worked this out on my personal web at nLab here, with supporting material linked to from this page.
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8
votes
Accepted
A question on the Grothendieck construction
The bicategory of elements of a Cat-valued functor is defined in e.g. Street's Fibrations in bicategories; it's the same as the usual one, with 2-cells as described here. Its property of classifying …
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3
votes
Terminology: lax vs. oplax colimits
Well, the smarmy answer is that it's neither, because you haven't given it a universal property. What you have is what I would call an oplax (co)cone, an 'oplax' transformation $X \Rightarrow \Delta_ …
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