Full paper in PDF:
$% C. Léger, Opérations sur les cartes et métamorphoses de la catégorie des G-ensembles,
Rev. Mat. Univ. Complut. Madrid 4 (1991), no. 1, 45–51.%$
Opérations sur les cartes et métamorphoses de la catégorie des G-ensembles
We call metamorphosis of a given category an autoequivalence functor. up to
within natural equivalence. We show that, given a group
, the group of
metamorphoses of the category of
-sets (as well as the corresponding group
for “sufficiently big” subcategories) may be naturally identified to the group of
outer automorphism of
. 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.
1991 Mathematics Subject Classification: 18A22, 52B70, 51A10.