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Results tagged with semigroups-and-monoids
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user 152679
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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"Tietze-like transformations" for defining interesting bijections between algebraic structures
Tietze transformations for arbitrary algebraic theories (with respect to their presentations) have been considered in Malbos–Mimram's Homological Computations for Term Rewriting Systems, in the contex …
- 10.7k
3
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Reference for the monoidal category structure $X \otimes Y = X + Y + X \times Y$ on a distri...
Given a distributive category $\mathscr C$ (more generally a rig category), we can define a (semicocartesian) monoidal category structure on $\mathscr C$ with tensor product given by $X \otimes Y := X …
- 10.7k