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Results tagged with higher-category-theory
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user 10605
For questions involving one or more categorical dimensions, or involving homotopy coherent categorical structures.
1
vote
A slicker proof that an object must be initial
The definition of object being initial is obviously equivalent to the statement "the inclusion of one-point category is final". Here by final functor I mean $p: I\to C$, such that for any $F: C\to D$ …
- 4,780
2
votes
Accepted
Local smallness and (higher) topoi
Consider a theory which has no models in $\mathrm{Set}$, but has a model in $\mathrm{Sh}(L)$ for some locale $L$. For example, the theory $\mathcal{CLF}$ of complete linearly ordered fields with more …
- 4,780
3
votes
(Co)limits of locally cartesian closed categories
I was talking about the following tentative argument. The 2-category of distributors (also called profunctors) $\mathrm{Dist}$ has (small) categories for objects. For $C,D:\mathrm{Dist}$ the 2-categor …
- 4,780
10
votes
Accepted
Automorphisms of Eilenberg-Mac Lane spaces and semidirect products (and the odd line)
As per Qiaochu Yuan's comment we need to only understand the space of based maps between $K(A,n)$ with a chosen base point.
The loop-deloop pair of functors establish an equivalence between the categ …
- 4,780
3
votes
3
answers
3k
views
Exact sequences in homotopy categories
I am not really familiar with homotopical category theory, so please forgive me if I make rude mistakes. I know quite a bit of common category theory, as well as familiar with algebraic topology.
How …
- 4,780