# Questions tagged [semigroups-and-monoids]

A semigroup is a set $S$ together with a binary operation that is associative. Examples of semigroups are the set of finite strings over a fixed alphabet (under concatenation) and the positive integers (under addition, maximum, or minimum). A monoid is a semigroup with a neutral element. Of course, any group is also a monoid/semigroup.

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### Can every cancellative invertible-free monoid be embedded in a group?

A monoid is invertible-free if $xy=1$ implies $x=y=1$ for all $x,y$. Question: Can every cancellative invertible-free monoid be embedded in a group? I'm fairly sure that a quotient of the free product ...
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### Extending a monoid object in a category

A monoid object in a pointed category $\mathcal{C}$ is an object $M$ equipped with a multiplication morphism $\mu: M\times M\to M$ that is associative and unital, meaning that the diagrams that ...
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### Classifying spaces of amalgamated topological monoids

Let $\mathsf{Top}_*$ be the category of well-based spaces and $\mathsf{TopMon}$ the category of topological monoids. Recall the James construction $\mathcal{J}:\mathsf{Top}_*\to \mathsf{TopMon}$ which ...
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### On the width of the Catalan monoid and the rank of K-groups of the Furstenberg transformation group

The semigroup algebra of the Catalan monoid is isomorphic to the incidence algebra of $P_n$, where $P_n$ is the poset consisting of subsets of { 1,...,n } where for two subsets $X \leq Y$ if and only ...
The question was asked on Mathematics Stackexchange but has remained unanswered so far. A self-map is a map $f:X\to X$ from a set $X$ to itself. There is an obvious notion of morphism, and thus of ...
I came across the following semi-group and the associated finite dimensional semi-group algebras over a field $K$ (which are Nakayama algebras) as they have very nice homological properties. My ...