# Tagged Questions

**4**

votes

**1**answer

90 views

### A terminal coalgebra of a certain functor on Mes

Let $\mathfrak C = \mathsf{Mes}$ be the category of meausurable spaces and measurable maps. For any object $X\in \mathfrak C_0$ we assign a measurable space $\mathcal P(X)$ whose elements $\mu$ are ...

**5**

votes

**2**answers

254 views

### Free cocommutative commutative Hopf monoids

I have some questions about generalizations of abelian groups, relative to symmetric monoidal categories.
1) Let $C$ be a cocomplete cartesian monoidal category with equalizers. I can show that the ...

**1**

vote

**1**answer

235 views

### (Co)Universal Property of Quotients/Subs

I'm not completely sure if this bunch of questions is the appropriate Level of MO. However at the same time I think that it is at least slightly above the level of stackex. ...
The tensor algebra ...

**7**

votes

**1**answer

556 views

### What extra conditions are necessary for the following version of Koszul duality?

Conventions: So that I don't have to worry about, fix a field $k$ of characteristic zero, and always work over it. Categories of modules, etc., are always $\infty$-categories of dg modules. ...

**2**

votes

**1**answer

147 views

### Is there a simple description of the indecomposable dg cocommutative coalgebras?

Let $\mathcal C$ be a closed symmetric monoidal category. By $\operatorname{Cog}(\mathcal C)$ I denote the category of cocommutative (counital coassociative) coalgebras in $\mathcal C$. Suppose that ...

**9**

votes

**1**answer

503 views

### Why not _co_free modules?

Let $R$ be a ring, and $R\text{-Mod}$ its category of all left modules. There is a "forgetful" functor $\operatorname{Forget}: R\text{-Mod} \to \text{AbGp}$, which is additive, continuous, and ...

**3**

votes

**1**answer

129 views

### Maximal subcoalgebras of an $F+1$-coalgebra corresponding to an $F$-coalgebra

This context of this question is Rutten's Universal Coalgebra, used for modelling systems. I'm interested in finding a description of a functor between different types of coalgebras corresponding to ...

**5**

votes

**0**answers

183 views

### “Question-answer” bisimulation

I often come across relations that would be defined as a bisimulation, except that the label match can be "inexact", that is, in the bisimulation game, a move labelled with "a" can be replied to with ...

**7**

votes

**1**answer

560 views

### Does the Tannaka-Krein theorem come from an equivalence of 2-categories?

Possibly the correct answer to this question is simply a pointer towards some recent literature on Tannaka-Krein-type theorems. The best article I know on the subject is the excellent
AndrĂ© Joyal ...

**1**

vote

**2**answers

286 views

### In which categories is every coalgebra a sum of its finite-dimensional subcoalgebras?

Let $\mathcal V$ be a reasonably nice category — I'm interested in the case when $\mathcal V$ is $\mathbb K$-linear for some field $\mathbb K$, abelian, and has all products and coproducts ...