Geodesic
Topos theoretic aspects of semigroup actions
Theory and applications of categories, Tome 24 (2010), pp. 117-147

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

We define the notion of a torsor for an inverse semigroup, which is based on semigroup actions, and prove that this is precisely the structure classified by the topos associated with an inverse semigroup. Unlike in the group case, not all set-theoretic torsors are isomorphic: we shall give a complete description of the category of torsors. We explain how a semigroup prehomomorphism gives rise to an adjunction between a restrictions-of-scalars functor and a tensor product functor, which we relate to the theory of covering spaces and E-unitary semigroups. We also interpret for semigroups the Lawvere-product of a sheaf and distributio$ and finally, we indicate how the theory might be extended to general semigroups, by defining a notion of torsor and a classifying topos for those.

Classification : 18B25, 18B40, 20M18, 20L05
Keywords: inverse semigroup, semigroup action, torsor, classifying topos 
@article{TAC_2010_24_a5,
     author = {Jonathon Funk and Pieter Hofstra},
     title = {Topos theoretic aspects of semigroup actions},
     journal = {Theory and applications of categories},
     pages = {117--147},
     publisher = {mathdoc},
     volume = {24},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2010_24_a5/}
}
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Jonathon Funk; Pieter Hofstra. Topos theoretic aspects of semigroup actions. Theory and applications of categories, Tome 24 (2010), pp. 117-147. http://geodesic.mathdoc.fr/item/TAC_2010_24_a5/