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-1 votes
1 answer
110 views

Variety of commutative semi group [closed]

V is a variety of commutative semi group satisfying the identity $x^2 = x^3$. I need to prove that: $|F_V(\{x_1\dots,x_n\})|$ = $3^n -1$. Any hints on this ? $F_V$ is V-free algebra.
Alvis's user avatar
  • 155
-2 votes
1 answer
314 views

configuration space and iterated loop space

Let the topological monoid $M$ be the configuration space $C(\mathbb{R}^n;X)=C_n(X)$ as in the book The geometry of iterated loop spaces, Theorem 5.2. I want to prove that the map $\alpha_n$ in ...
Shiquan Ren's user avatar
  • 1,990
-2 votes
1 answer
780 views

commutative monoids have binary products? [closed]

Does the category CMonoid of commutative monoids have binary products? thanks
lala's user avatar
  • 1
-3 votes
1 answer
234 views

A common name for a functorial construction of Commutative Algebra?

I am interested whether the following construction naturally appearing in Commutative Algebra has some know and acceped name. Given a commutative monoid $(M,+)$ and a set $X$, consider the family $F(...
Taras Banakh's user avatar
  • 41.9k
-4 votes
1 answer
224 views

Do monoid homomorphisms from $X^X$ to a group factor through $\text{Sym}(X)$? [closed]

Let $X$ be a set and let $(X^X,\circ)$ denote the monoid of all maps $f: X\to X$, together with composition. Let $(\text{Sym}(X),\circ)$ be the group of all bijections from $X$ to itself. Does there ...
Dominic van der Zypen's user avatar
-8 votes
1 answer
351 views

Are there overwhelmingly more finite monoids than finite spaces? [closed]

A function $f:\mathbb{Z}_{\geq 1}\to\mathbb{Z}_{\geq 1}$ overwhelms $g:\mathbb{Z}_{\geq 1}\to\mathbb{Z}_{\geq 1}$ if for any $k\in \mathbb{Z}_{\geq 1}$ the inequality $f(n)\leq g(n+k)$ holds only for ...
firn's user avatar
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