Search Results

The following fact seems to be implicitly used in the proof of (4)$\implies$(5) of Theorem 5.5.1.1 of Lurie's Higher Tops Theory: Let $\kappa$ be a small regular cardinal, and let $\mathcal{C}$ be a …

The density theorem in the ordinary category theory asserts that every presheaf on a small category is a colimit of representables in a canonical way. In Lemma 5.1.5.3 of Higher Topos Theory, Lurie pr …

This is similar to another question on MO, but is different. Let $p:\mathcal{E}\to\mathcal{C}$ be a right fibration between $\infty$-categories. As explained in Lurie's HTT, $\S$2.1, we can consider $ …

While playing around with $\infty$-categories, I ran into the following problem: Let $p:\mathcal{C}\to\mathcal{D}$ be a functor of $\infty$-categories. Does one of the following condition imply the o …

I have a question regarding the proof of Proposition 2.19 of Factorization homology of topological manifolds by Ayala and Francis. In the final paragraph of the proof (more specifically, in the second …

Let $\mathcal{C}$ and $\mathcal{D}$ be $\infty$-categories (by which I mean quasicategories, though I suspect that it hardly matters), and let $n\geq 1$ be an integer. There is a functor $$\theta:\ope …

This is a question on seemingly equivalent definitions of relative limits, formulated in the language of quasi-categories. I will use notations from Higher Topos Theory. Let $p:\mathcal{C}\to\mathcal …

In his book Higher Algebra, Lurie introduces the notion of generalized $\infty$-operads ($\S$2.3.2). Roughly speaking, a generalized $\infty$-operad is a "family" of $\infty$-operads parametrized by a …

I do not understand the proof of Variant 4.2.3.16 of Higher Topos Theory by Jacob Lurie, and I need help. Variant 4.2.3.16 asserts the following: ($\diamond$) Let $K$ be a finite simplicial set. The …

In Proposition 7.2.1.14 of Higher Topos Theory, Lurie asserts the following: Let $\mathcal{X}$ be an $\infty$-topos and let $\tau_{\leq0}:\mathcal{X}\to\tau_{\leq0}\mathcal{X}$ denote a left adjoint …

In his book Higher Topos Theory, Lurie proves that in some favorable cases, functor categories of $\infty$-categories admits a rigid model. More precisely, he proves in Proposition 4.2.4.4 the followi …

Let $\mathcal{M}\mathrm{fld}_n$ denote the $\infty$-category of topological manifolds (without boundary) and embeddings; more precisely, it is the homotopy coherent nerve of the simplicial category wh …

Let $\mathcal{A}$ and $\mathcal{B}$ be presentably symmetric monoidal $\infty$-categories, i.e., symmetric monoidal $\infty$-categories whose underlying $\infty$-category are presentable and whose ten …

Let $\mathcal{C}$ be a small $\infty$-category. Using the straightening-unstraightening construction, we can define a hom-functor of $\mathcal{C}$ as a functor $\mathcal{C}(-,-):\mathcal{C}^{\mathrm{o …

I am reading the proof of Propositions 2.3.4.5 of Higher Algebra by Jacob Lurie. There is a part that I don't understand, and I need someone's help. In the book, Lurie introduces the notion of familie …