All Questions
Tagged with monads infinity-categories
7 questions
9
votes
1
answer
432
views
Two definitions of a monad on an ∞-category
In the literature on $\infty$-categories (quasi-categories) I found two different definitions of a monad on an $\infty$-category, and I don't understand the relation between them.
The first ...
- 1,484
7
votes
1
answer
281
views
Finitely presentable objects in the categories of algebras of $\infty$-algebraic theories
By default, all terms are understood in the infinity sense (“category” means “$(\infty, 1)$-category”, etc.).
An object $A$ in a category is said to be finitely presentable (or compact) if the functor ...
- 6,962
26
votes
1
answer
2k
views
Infinity-categorical analogue of compact Hausdorff
Recently I became through this mathoverflow question aware of the article Codensity and the ultrafilter monad by Tom Leinster. There he shows that the ultrafilter monad on the category $\mathrm{Set}$ ...
- 12.1k
5
votes
0
answers
70
views
Does the restriction functor $j^* $ to Zariski open preserve the limit of $j^*$-split cosimplicial diagram?
This might be a trivial question but I could not find a satisfatory answer easily.
Let $X = \mathbb{C}$ and $U = \mathbb{C}^*$, and let $j: U \to X$ denote the open embedding.
Consider $j^* : QCoh(X) \...
- 51
2
votes
0
answers
76
views
Diagrammatic model for free product in monad infinity category
$\newcommand{\C}{\mathcal{C}}$ Suppose $M$ is a monad in an $\infty$-category $\C,$ and $A, B$ are two algebras over $M$. I'm willing to assume any reasonable "niceness" conditions on $\C$, $...
- 7,972
6
votes
1
answer
560
views
Higher descent cohomology
Descent cohomology for a comonad is defined at degrees 0 and 1 by Mesablishvili in his paper "On Descent Cohomology" (as well as by many other authors in many other contexts). For a comonad $\bot$ on ...
- 10.5k
10
votes
0
answers
252
views
Colimits of algebras for $\infty$-Monad
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 ...
- 42.4k