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A pushout $B \coprod_A C$ will almost never have all coproduct. the problem is that objects in $B \coprod_A C$ are all either objects of $B$ or objects of $C$, so if $B \coprod_A C$ has coproduct, it …

I would like to know in anyone has developed method for constructing colimits in the category of algebra for a monad in the $(\infty,1)$-categorical framework, using transfinite constructions. I have …

(note: this question is essentially a reference request for the tensor product described at the end. the rest is context) It is well known that the category of chain complexes (in positive degree, wi …

If you don't mind, I'll talk about strinct $\infty$-categories, but weak $(\infty,n)$-category to avoid discussing the 'problem' regarding the non uniqueness of the meaning of $(\infty,\infty)$-catego …

One has a nice "folk" model structure on strict $\infty$-categories due to Yves Lafont, Francois Metayer and Krzysztof Worytkiewicz whose notion of weak equivalences seem to be the notion of weak equi …

In short there isn't: the problem is that if you just have globular sets - and if you want $k$-cells to model $k$-arrows following the globular structure - then globular sets have no way of expressing …

In $1$-category theory, a well pointed endofunctor of a category $C$, is an endofunctor $F:C \rightarrow C$ endowed with a natural transformation $\sigma : Id \rightarrow F$ such that the two natural …

This is just an expended version of the comment. The answer to the question as asked is no. The problem is that for any ($\infty$-)category $J$ the category $D_J$ of functors $J \to Cat_\infty$ that a …

There is a bit of notation to be careful about here: $\mathcal{X}_{\leqslant 1}$ is often used to denote the full subcategory of $\mathcal{X}$ of set-truncated object. For example if $\mathcal{X}$ is …

It is in general not too hard to show that maps between finite $CW$-complexes/finite simplicial sets are homotopy equivalences. Question : Can we do something similar for: quasi-categorical equival …

Well, it is easy to give definitions, the problem is finding the "right" one. Here "right" can mean that gives the correct notion up to homotopy (many definition will be equivalent) but also it can me …

Let me clarify a bit what I meant in my comment on how the notion of bilinearity will depends on "how commutative" are $A$, $B$ and $C$, and this is one way to define a hierarchy of notion of bilinear …

Let $G$ be a locally compact topological group (or more generally a localic group). Is there an infinity topos which classify principal $G$ bundles ? More precisely, is there an $\infty$-topos $BG$ s …

Probably not the best one can do, and what follows might be a bit 'overkill', but it answer the question about dependency on universe, and it is a nice argument. Also if you know how the proof of th …

I'm trying to get more intiution about higher K-theory, Hochschild homology and the trace map between by thinking about these objects from an informal $\infty$-categorical perspective, instead of usin …