Semigroup Actions on Sets and the Burnside Ring

@article{Erdal2018SemigroupAO,
  title={Semigroup Actions on Sets and the Burnside Ring},
  author={Mehmet Akif Erdal and {\"O}zg{\"u}n {\"U}nl{\"u}},
  journal={Applied Categorical Structures},
  year={2018},
  volume={26},
  pages={7-28}
}
In this paper we discuss some enlargements of the category of sets with semigroup actions and equivariant functions. We show that these enlarged categories possess two idempotent endofunctors. In the case of groups these enlarged categories are equivalent to the usual category of group actions and equivariant functions, and these idempotent endofunctors reverse a given action. For a general semigroup we show that these enlarged categories admit homotopical category structures defined by using… 
Stabilization and costabilization with respect to an action of a monoidal category
Given a monoidal category V that acts on a 0-cellA in a 2-category M, we give constructions of stabilization and costabilization of A with respect to the V-action. This provide a general unified
Monoid actions, their categorification and applications
MONOID ACTIONS, THEIR CATEGORIFICATION AND APPLICATIONS Mehmet Akif Erdal Ph.D. in Mathematics Advisor: Özgün Ünlü December, 2016 We study actions of monoids and monoidal categories, and their
Homotopical categories of spaces with monoid actions
Let $M$ be a monoid. We construct a family of homotopical category structures on the category of $M$-spaces. Moreover, we show that each of these homotopical categories is a Brown's category of
An Elmendorf-Piacenza type Theorem for Actions of Monoids
Let M be a monoid and G : Mon → Grp be the group completion functor from monoids to groups. Given a collection Z of submonoids of M and for each N ∈ Z a collection YN of subgroups of G(N), we
Alexandroff topologies and monoid actions
Abstract Given a monoid S acting (on the left) on a set X, all the subsets of X which are invariant with respect to such an action constitute the family of the closed subsets of an Alexandroff
Approximating monoid actions by group actions.
Let $M$ be a monoid. We construct a family of model structures on the category of $M$-spaces. The weak equivalences of these model categories are defined by using the universally assigned groups
Reversing monoid actions and domination in graphs
. Given a graph G = ( V,E ), a set of vertices D ⊆ V is called a dominating set if every vertex in V \ D is adjacent to a vertex in D , and a subset B ⊆ V is called a nonblocking set if V − B is a

References

SHOWING 1-10 OF 18 REFERENCES
Transformation groups and representation theory
The Burnside ring of finite G-sets.- The J-homomorphism and quadratic forms.- ?-rings.- Permutation representations.- The Burnside-ring of a compact Lie group.- Induction theory.- Equivariant
Elliptic Curves as Attractors in ℙ2 Part 1: Dynamics
TLDR
It is proved that the genus-one curve (a topological torus) can never have a trapping neighborhood, yet it can have an attracting basin of large measure (perhaps even of full measure).
Biset Functors for Finite Groups
Examples.- General properties.- -Sets and (, )-Bisets.- Biset Functors.- Simple Functors.- Biset functors on replete subcategories.- The Burnside Functor.- Endomorphism Algebras.- The Functor.-
A characterisation of solvable groups
Let G be a finite group. A G-set M is a finite set on which G operates from the left by permutations, i.e. a finite set together with a map G • (g, m) ~ g m with g(h m)= (g h) m, e m = m for g, h, ee
Homotopy Limit Functors on Model Categories and Homotopical Categories
Model categories: An overview Model categories and their homotopy categories Quillen functors Homotopical cocompleteness and completeness of model categories Homotopical categories: Summary of part
Global attractors for semigroup actions
Transformation of Groups
In this work, we have proved a number of purely geometric statements by algebraic methods. Also we have proved Sylvester’s law of Nullity and Exercise: the nullity of the product BA never exceeds the
Toposes Are Adhesive
TLDR
The study of adhesive categories is continued by showing that toposes are adhesive, which relies on exploiting the relationship between adhesive categories, Brown and Janelidze's work on generalised van Kampen theorems as well as Grothendieck's theory of descent.
...
...