# Tagged Questions

**2**

votes

**1**answer

55 views

### Does the category PCM (partial commutative monoids) have a closed symmetric monoidal product?

A partial commutative monoid (PCM) is, roughly speaking, a set with a partially defined binary operation that is as associative as it can be (given that not all products are defined) and commutative. ...

**1**

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**2**answers

105 views

### Comonads from monoids

The following construction is probably known. I think it should work in any closed symmetric monoidal category, but I will play it safe and formulate the question in the concrete, cartesian closed ...

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**0**answers

60 views

### Monoid action on an uncountably infinite set

The action of a monoid on a finite set is equivalent to a finite state machine, however I would like a categorical way to think about an uncountably infinite state machine (a state transition ...

**2**

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**2**answers

95 views

### Locally finite varieties which are not finitely generated

Let $\Sigma$ be a signature consisting of operations with finite arity. Let $\mathcal{V}$ be a variety of algebras for this signature. Further suppose that $\mathcal{V}$ is locally finite i.e. every ...

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**2**answers

284 views

### Are algebraic structures uniquely identifed by their free objects?

It might be a naive question, as I am not a specialist in this field.
This is a follow-up to this question.
I want to study varieties of objects generalizing ordered monoids, in particular using an ...

**2**

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**2**answers

139 views

### Equivalence relations in suplattices

I am wondering about generalisations of the concept of equivalence relations to suplattices.
Here is my motivation: Given a set $X$. The powerset $\mathcal{P}(X)$ is a suplattice. For suplattices ...

**5**

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**2**answers

441 views

### What is the free monoidal category generated by a monoid?

In several places in a segment on cohomology (for example, here (PDF)) in John Baez's online lecture notes for a course in 2007 on quantum gravity, much is made of the fact that the simplex category ...

**15**

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**1**answer

483 views

### Toposes (topoi) as classifying toposes of groupoids

A famous theorem of Joyal and Tierney says that each Grothendieck topos is equivalent to the classifying topos of a localic groupoid. I believe that Buntz and Moerdijk have shown that if the topos has ...

**14**

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**0**answers

597 views

### Is the category of smooth manifolds equivalent to the opposite category of the category of commutative monoids of some additive symmetric monoidal category?

This is a followup to my previous question, which asked whether
the category of commutative or noncommutative C*-algebras or von Neumann algebras
is equivalent to the category of commutative or ...

**4**

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**0**answers

221 views

### When is the cofibrant replacement of a product the product of the cofibrant replacements?

I'm in a situation where I'd like to prove $Q(E\otimes E) \simeq QE \otimes QE$ for a monoid $E$ in a symmetric monoidal model category. I know it's not true in general that $Q(E\otimes F)\simeq QE ...

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**5**answers

592 views

### Monoids with infinite products

Say a monoid $M$ has infinite products if, for any (possibly infinite) sequence $(m_1,m_2,\ldots)$ of elements of $M$, there exists an element $m_1m_2\cdots\in M$, satisfying some good properties. ...

**5**

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**0**answers

326 views

### Chain/Hierarchy of Monoids

Let's assume that we have the following collection of structures:
Some space $P$.
Monoids $(M_{i+1},\circ_{i+1})$, and
Actions $\bullet_{i+1}:M_{i+1}\times M_i\to M_i$, for $i\ge 0$
And ...

**9**

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**4**answers

754 views

### Why is a monoid with closed symmetric monoidal module category commutative?

Given a symmetric monoidal category and a monoid object A in it, one can form the category of modules over this monoid object, i.e. objects are $A \otimes M \rightarrow M$ satisfying the natural ...

**12**

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**3**answers

590 views

### Model Structure/Homotopy Pushouts in topological monoids?

Let C be the category of topological monoids, that is, the category of monoids in (Top, $\times$).
Can the model category structure on Top (Serre fibrations, cofibrations, weak homotopy ...

**11**

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**2**answers

688 views

### Recovering a monoidal category from its category of monoids

What kind of additional properties and/or structures one needs to impose on the category
of (commutative or noncommutative) monoids of some monoidal category
so that one can recover the original ...