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Let $k$ be a commutative ring with $1$, and let $\mathsf{dgCat}_k$ be the category of $k$-linear dg-categories, as defined in [1, Section 2]. We may equip $\mathsf{dgCat}_k$ with the Morita model ...

I am trying to reduce the computation of weak operadic colimits to colimits. Let me introduct some notation. Let $q:C^{\otimes} \to N(Fin_*)$ be a symmetric monoidal category. Let $p: K \to C^{\...

Let $C$ be a combinatorial symmetric monoidal model category and let $A$ be a associative algebra object in $C$, that is cofibrant as an object in $C$. In Higher Algebra 4.3.3.17, Lurie proves an ...

There are several notions of nerves, including nerves of categories, $2$-categories, and simplicial categories. These define functors \begin{align*} \mathrm{N} &\colon \mathrm{Cats}_{(2,1)} ...