Commutativity in Double Interchange Semigroups
نویسندگان
چکیده
منابع مشابه
Note on Commutativity in Double Semigroups and Two-fold Monoidal Categories
A concrete computation — twelve slidings with sixteen tiles — reveals that certain commutativity phenomena occur in every double semigroup. This can be seen as a sort of EckmannHilton argument, but it does not use units. The result implies in particular that all cancellative double semigroups and all inverse double semigroups are commutative. Stepping up one dimension, the result is used to pro...
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Double semigroups have two associative operations ◦, • related by the interchange relation: (a • b) ◦ (c • d) ≡ (a ◦ c) • (b ◦ d). Kock [13] (2007) discovered a commutativity property in degree 16 for double semigroups: associativity and the interchange relation combine to produce permutations of elements. We show that such properties can be expressed in terms of cycles in directed graphs with ...
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ژورنال
عنوان ژورنال: Applied Categorical Structures
سال: 2018
ISSN: 0927-2852,1572-9095
DOI: 10.1007/s10485-018-9531-5