Search Results

Suppose that $\mathscr{C}$ is a $2$-category (or more generally a bicategory) which is not a $\left(2,1\right)$-category. Is there any relation between limits and colimits in $\mathscr{C}$ (in the wea …

Suppose that $\mathscr{P}$ is a (locally) presentable $\left(\infty,1\right)$ category (which we can assume WLOG is infinity presheaves on some small $\left(\infty,1\right)$ category) , and $R$ and $S …

What he means is, in this context, since you are considering psuedofunctors into the 2-category of groupoids where all 2-cells are invertible, lax functors are the same as pseudofunctors. The more mod …

If $F:C \to D$ is a Cartesian fibration of $\infty$-categories, I would like to show that $F$ preserves pullbacks. This seems intuitively clear, but I haven't found it in HTT (but perhaps I missed it) …

If $C$ is a category of fibrant objects, is its associated $\infty$-category idempotent complete, i.e. is it accessible? If this is not always true, besides from the case when it is an $n$-category fo …

The notion of a Grothendieck fibration in the 2-category $CAT$ of small categories, can be written down to make sense for any 2-category, and such a morphism in a 2-category is called a fibration: ht …

If $\mathcal{C}$ is a category and $\lambda:\Delta_D \to id_{\mathcal{C}}$ is a cone for the identity functor, and $F:J \to \mathcal{C}$ is a functor such that $F\lambda:\Delta_D \to F$ is a limiting …

Given an infinity topos $\mathcal{E}$, one can pass to its hypercompletion $\widehat{\mathcal{E}}$, which is the full subcategory on those objects local with respect to $\infty$-connected morphisms (m …

It is well known that for ordinary categories, if $C$ has finite limits and $D$ is cocomplete, and $A:C \to D $ is left-exact (i.e. preserves finite limits) then the left-Kan extension of $F$ along t …

For reference, at least when $D$ is an infinity topos, which I believe is probably necessary, this is Proposition 6.1.5.2 in HTT.

Ok, so I have an argument: First note that the homotopy coherent nerve of $\mathit{Mfd}_W$ is equivalent to the quasicategory obtained by formally inverting $W$ in $N\left(\mathit{Mfd}\right)$- this …

Suppose that $(C,J)$ and $(D,K)$ are two Grothendieck (possibly $\infty$-)sites and $f:C \to D$ is a functor such that $$f^*:Psh(D) \to Psh(C)$$ sends sheaves to sheaves. Under what conditions will $$ …

This question may be a bit vague, (so if suggested, can I make it community wiki), but I was wondering what techniques there exists for computing homotopy colimits in a category of fibrant objects. A …

You asked about a category of fractions, so it sounds to me like you really want to formally invert the arrows in $W$. For that, you want something different than what Urs is explaining, however, the …

In the quasi-category formalism of $(\infty,1)$-categories, it is hard to make sense of whether they are strictly enriched, or weakly enriched in infinity-groupoids. This is mostly due to the ambiguit …