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Results tagged with infinity-categories
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user 57280
Part of higher category theory that for instance in Algebraic Topology enables us to capture finer homotopic distinctions. As in say Eilenberg-Maclane spaces.
4
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2
answers
488
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Pullbacks and fibers in the $\infty$-category of spaces
Suppose given a commutative diagram in the $\infty$-category of spaces, as the one depicted below, where all but the bottom-right squares are pullbacks. Is it true that $H$ is (equivalent to) the fibe …
- 16.5k
10
votes
1
answer
659
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On HTT's Lemma 3.3.4.1
While studying the book Higher Topos Theory I have encountered some difficulty with Lemma 3.3.4.1, which says that the pullback along a cartesian fibration of a map q such that $q^{op}$ is cofinal is …
- 13.5k
7
votes
2
answers
389
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Equivalent definitions of Cartesian Fibrations between Quasi-Categories
In the paper by Verity and Riehl "Fibrations and Yoneda lemma in an ${\infty}$-cosmos" (https://arxiv.org/abs/1506.05500), they prove a Yoneda lemma that holds in any ${\infty}$-cosmos (see Corollary …
- 1,947
8
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0
answers
260
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A completeness criterion for $\infty$-categories
We all know that for ordinary categories $\mathscr{C}, \mathscr{D}$ (with $\mathscr{C}$ small) the limit of a functor $F:\mathscr{C} \to \mathscr{D}$, if it exists, can be constructed by using product …
- 1,403
2
votes
0
answers
83
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Cancellation property of groupoidal cartesian fibrations
I have an issue concerning a property of "left cancellation" for groupoidal cartesian fibrations of ∞-cosmoi (but everything works fine in a 2-category as well).
A 1-cell $p: E \to B$ is called group …
- 1,403
3
votes
1
answer
140
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Segal maps for Segal precategories
A Segal precategory is just a simplicial space $X:\Delta^{op} \to sSet$ such that its $0$-th space is discrete (i.e. constant). A Segal category is defined everywhere in the literature as a Segal prec …
- 52.6k
13
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1
answer
594
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Lemma 2.1.1.4 in Lurie's HTT
I have encountered a problem in understanding Lurie's proof of the following fact:
"Given a left fibration between simplicial sets $q:X \to S$, there exists a functor $$ho(S) \to Ho(sSet)$$ which is …
- 13.5k
2
votes
1
answer
245
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Is the discrete nerve of a small category a complete Segal space?
While reading Rezk's paper "A model for the homotopy theory of homotopy theory", I found a remark which contradicts a guess of mine, but I can't see where I am wrong (perhaps it might be a silly mista …
- 1,609
0
votes
1
answer
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Clarification about Joyal's notation [closed]
At the very beginning of chapter 5 of Joyal's lectures on Quasi-Categories (http://mat.uab.cat/~kock/crm/hocat/advanced-course/Quadern45-2.pdf), he uses a notation which I think he has never explained …
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