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Reedy categories which encode the notion of category actions

Julia E. Bergner, Philip Hackney (2015)

Fundamenta Mathematicae

We study a certain type of action of categories on categories and on operads. Using the structure of the categories Δ and Ω governing category and operad structures, respectively, we define categories which instead encode the structure of a category acting on a category, or a category acting on an operad. We prove that the former has the structure of an elegant Reedy category, whereas the latter has the structure of a generalized Reedy category. In particular, this approach gives a new way to regard...

Reflection loops of spaces with congruence and hyperbolic incidence structure

Alexander Kreuzer (2004)

Commentationes Mathematicae Universitatis Carolinae

In an absolute space ( P , 𝔏 , , α ) with congruence there are line reflections and point reflections. With the help of point reflections one can define in a natural way an addition + of points which is only associative if the product of three point reflection is a point reflection again. In general, for example for the case that ( P , 𝔏 , α ) is a linear space with hyperbolic incidence structure, the addition is not associative. ( P , + ) is a K-loop or a Bruck loop.

Regular, inverse, and completely regular centralizers of permutations

Janusz Konieczny (2003)

Mathematica Bohemica

For an arbitrary permutation σ in the semigroup T n of full transformations on a set with n elements, the regular elements of the centralizer C ( σ ) of σ in T n are characterized and criteria are given for C ( σ ) to be a regular semigroup, an inverse semigroup, and a completely regular semigroup.

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