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Results tagged with higher-category-theory
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user 76299
For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
7
votes
1
answer
161
views
When is the category of sheaves on a site compactly assembled/a continuous category?
If $(C,J)$ is a site, what is a natural condition on the Grothendieck topology $J$ to ensure that the category $Sh(C,J)$ is compactly assembled? I am both interested in the 1-categorical as well as th …
- 2,303
18
votes
0
answers
310
views
The analogy between dualizable categories and compact Hausdorff spaces
Efimov has in his recent preprint K-theory and localizing invariants of large categories, Appendix F, a long table of analogies between the categories $\text{Cat}^\text{dual}_\text{st}$ and $\text{Com …
- 2,303
10
votes
1
answer
392
views
Definition of $Fun^G( \mathcal C, \mathcal D)$ in the setting of quasicategories
Our research group is currently going through the paper by Thomas Nikolaus and Peter Scholze On Topological Cyclic Homology and in the Appendix B, Proposition B.5., they use the notation $Fun^{B \math …
- 2,303
24
votes
1
answer
1k
views
Examples of $(\infty,1)$-topoi that are not given as sheaves on a Grothendieck topology
An $(\infty,1)$-topos according to Lurie is defined as (accessible) left exact localization of a presheaf $(\infty,1)$-category $\text{P}(\mathcal C)$.
Those $(\infty,1)$-topoi $\text{Sh}(\mathcal C)$ …
- 2,303
4
votes
1
answer
510
views
The "$\infty$"-column in the periodic table of n-categories
A monoid is the same as a category with a single object.
A monoidal category is the same as a bi-category with a single object.
A commutative monoid is the same as a bi-category with a single object …
- 2,303