# ct.category-theory's questions - English 1answer

3.840 ct.category-theory questions.

### 3 What is a spectrum object in $\infty$-topoi?

For any spectrum $E$, there is a "discrete" topos spectrum $(Spaces / E_n)_n$. And I believe any topos spectrum is a localization of a "discrete" one. Are there any "non-discrete" topos spectra? To ...

### 4 Categorifying Hyperoperations

Is there some categorical version of tetration or higher hyperoperations? This is motivated by the fact that coproducts categorify addition of finite cardinals, and products/exponentials categorify ...

### The multi-set monad and modules

I am trying to analyze the category of algebras for the finite free commutative monoid monad, aka the finite multiset monad. This monad is frequently described as having a multiplication that takes a ...

### 3 Is the category of inclusion prespectra bicomplete?

Working in compactly generated weak Hausdorff spaces, is the category of inclusion prespectra bicomplete? I should probably specify that by inclusion prespectra, I mean prespectra such that the ...

### 47 Does “finitely presented” mean “always finitely presented”? (Answered: Yes!)

Precisely, if an R-module M has a finite presentation, and Rk → M is some unrelated surjection (k finite), is the kernel necessarily also finitely generated? Basically I want to believe I can ...

### 7 Does each monotonic endofunctor on the category of sets and relations preserve conversion?

Consider a functor $F : \mathbf{Rel} \to \mathbf{Rel}$ that is monotonic (for all relations $R$ and $S$ with $R \subseteq S$ we have $FR \subseteq FS$). Does such a functor always preserve conversion ...

### 1 Axiomatization of the shuffle decomposition

I am trying to figure out an axiomatization for Reedy categories such that the product of representables admits a shuffle decomposition. Cisinski suggested imposing a condition, which we will state ...

### 5 Products of representables are regular on a regular skeletal Reedy category?

1 answers, 95 views ct.category-theory homotopy-theory
The definition of a (pre)regular skeletal Reedy category in the sense of Cisinski generalizes the intuition behind the Eilenberg-Zilber factorization for simplicial sets, specifically the property ...

### 4 What is the category of algebras for the finitely supported measures monad?

In this post, I was introduced to the monad of finitely supported measures. $HX$ is the set of finitely supported measures on $X$, with monad structure defined as for the Giry monad. I have three ...

### 10 Are there continua in $\infty$-topoi?

If topology were invented for algebraic geometry or logic, in ignorance of Euclidean space, we might reasonably regard connected compact Hausdorff spaces as pathological, or even doubt their existence....

### 26 Does the hypergraph structure of the set of subgroups of a finite group characterize isomorphism type?

Question Suppose there is a bijection between the underlying sets of two finite groups $G, H$, such that every subgroup of $G$ corresponds to a subgroup of $H$, and that every subgroup of $H$ ...

### 19 What is the geometric significance of fibered category theory in topos theory?

Often in topos theory, one starts with a geometric morphism $f: \mathcal Y \to \mathcal X$, but quickly passes to the Grothendieck fibration $U_f: \mathcal Y \downarrow f^\ast \to \mathcal X$, which ...

### 10 What is the correct definition of localisation of a category?

Disclaimer: I wasn't sure if this was an appropriate question for MathOverflow, and so I've also asked this on StackExchange. There appears to be a discrepancy in the literature regarding the ...

### 6 Virtual generators

Let $\mathcal{K}$ be a category. Prop 1. If $\mathcal{K}$ has a (strong) generator then there is a faithful (and conservative) functor $U: \mathcal{K} \to \text{Set}$ preserving connected limits. ...