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5
votes
0answers
329 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 ...
-1
votes
1answer
507 views

commutative monoids have binary products? [closed]

Does the category CMonoid of commutative monoids have binary products? thanks
1
vote
1answer
1k views

Does the category Monoid of monoids have finite coproducts?

Does the category Monoid of monoids have finite coproducts?
12
votes
2answers
440 views

How do you compute the space of lifts of an E-infinity map?

Let X, Y and B be $E_\infty$ spaces, and let $p: X \rightarrow Y$ and $f: B \rightarrow Y$ be $E_\infty$ maps. We can ask for the space of lifts of f across p, that is the space of $E_\infty$ maps ...
10
votes
4answers
856 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 ...
1
vote
1answer
559 views

monoid ring and some structure within it - how is it called?

I am amateur - mathematics is my hobby, and I find some strange structure working with toy matrices structure so I try to ask some questions regarding it. Let me allow to introduce some structure ...
10
votes
6answers
1k views

Computing the structure of the group completion of an abelian monoid, how hard can it be?

Cherry Kearton, Bayer-Fluckiger and others have results that say the monoid of isotopy classes of smooth oriented embeddings of $S^n$ in $S^{n+2}$ is not a free commutative monoid provided $n \geq 3$. ...
12
votes
3answers
639 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 ...
12
votes
2answers
748 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 ...
16
votes
12answers
2k views

Homological Algebra for Commutative Monoids?

Homological algebra for abelian groups is a standard tool in many fields of mathematics. How much carries over to the setting of commutative monoids (with unit)? It seems like there is a notion of ...