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Results tagged with semigroups-and-monoids
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user 2327
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.
10
votes
Model Structure/Homotopy Pushouts in topological monoids?
It's easy to describe the group completion of a pushout, up to homotopy. If $Y\leftarrow X \rightarrow Z$ is the diagram of topological monoids, then the group completion of the pushout is equivalent …
- 967
7
votes
How do you compute the space of lifts of an E-infinity map?
If $Y$ and $B$ are grouplike, then the question, of course, immediately reduces to the case of spectra: The map $X\rightarrow B$ factors through the group completion $\Omega B X$ of $X$, so you can th …
- 967