We call metamorphosis of a given category an autoequivalence functor up to within natural equivalence. We show that, given a group G, the group of metamorphoses of the category of G-sets (as well as the corresponding group for ?sufficiently big? subcategories) may be naturally identified to the group of outer automorphism of G. We get by this way a natural description of a group of known operations on tessellations of a surface: the identity operation, the Poincaré duality, and four others which generally change the topological type of the surface.
@article{urn:eudml:doc:44293,
title = {Op\'erations sur les cartes et m\'etamorphoses de la cat\'egorie des G-ensembles.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {4},
year = {1991},
pages = {45-51},
zbl = {0753.18001},
mrnumber = {MR1142548},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44293}
}
Léger, Christian. Opérations sur les cartes et métamorphoses de la catégorie des G-ensembles.. Revista Matemática de la Universidad Complutense de Madrid, Tome 4 (1991) pp. 45-51. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44293/