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  2. Free monoid - Wikipedia

    en.wikipedia.org/wiki/Free_monoid

    The free monoid on a set A is usually denoted A ∗. The free semigroup on A is the subsemigroup of A ∗ containing all elements except the empty string. It is usually denoted A +. [1] [2] More generally, an abstract monoid (or semigroup) S is described as free if it is isomorphic to the free monoid (or semigroup) on some set. [3]

  3. Monoid - Wikipedia

    en.wikipedia.org/wiki/Monoid

    Many definitions and theorems about monoids can be generalised to small categories with more than one object. For example, a quotient of a category with one object is just a quotient monoid. Monoids, just like other algebraic structures, also form their own category, Mon, whose objects are monoids and whose morphisms are monoid homomorphisms. [8]

  4. Monoid (category theory) - Wikipedia

    en.wikipedia.org/wiki/Monoid_(category_theory)

    A monoid object in the category of monoids (with the direct product of monoids) is just a commutative monoid. This follows easily from the Eckmann–Hilton argument. A monoid object in the category of complete join-semilattices Sup (with the monoidal structure induced by the Cartesian product) is a unital quantale.

  5. Semi-Thue system - Wikipedia

    en.wikipedia.org/wiki/Semi-Thue_system

    For example, the alphabet {a, b} with the rules { ab → ε, ba → ε }, where ε is the empty string, is a presentation of the free group on one generator. If instead the rules are just { ab → ε }, then we obtain a presentation of the bicyclic monoid. The importance of semi-Thue systems as presentation of monoids is made stronger by the ...

  6. Numerical semigroup - Wikipedia

    en.wikipedia.org/wiki/Numerical_semigroup

    Numerical semigroups are commutative monoids and are also known as numerical monoids. [ 1 ] [ 2 ] The definition of numerical semigroup is intimately related to the problem of determining nonnegative integers that can be expressed in the form x 1 n 1 + x 2 n 2 + ... + x r n r for a given set { n 1 , n 2 , ..., n r } of positive integers and for ...

  7. Trace theory - Wikipedia

    en.wikipedia.org/wiki/Trace_theory

    In mathematics and computer science, trace theory aims to provide a concrete mathematical underpinning for the study of concurrent computation and process calculi.The underpinning is provided by an algebraic definition of the free partially commutative monoid or trace monoid, or equivalently, the history monoid, which provides a concrete algebraic foundation, analogous to the way that the free ...

  8. 9 Best Free Movie Watching Websites and Streaming Services - AOL

    www.aol.com/9-best-free-movie-watching-184537067...

    The best free movie services offer a wide variety of films and plenty of ways to watch them. Check out these top picks for alternatives to paid streaming services.

  9. Presentation of a monoid - Wikipedia

    en.wikipedia.org/wiki/Presentation_of_a_monoid

    The monoid is then presented as the quotient of the free monoid (or the free semigroup) by these relations. This is an analogue of a group presentation in group theory . As a mathematical structure, a monoid presentation is identical to a string rewriting system (also known as a semi-Thue system).