For any pair of categories (C, K) enriched over the category Gpd of groupoids, it is possible to define a strong shape category SSh(C, K) in such a way that, for C the category of topological spaces and K its full subcategory of spaces having the homotopy type of absolute neighborhoods retracts for metric spaces, one obtains the strong shape category SSh(Top) , as defined by Mardešić. We also introduce a new category SSK with the same objects as C and morphisms given by suitable pseudo-natural transformations into the category of groupoids. The main result is then that such a category SSK is isomorphic to the strong shape category SSh(C, K) , when C is also a proper model category.
Strong shape in categories enriched over groupoids
Stramaccia, Luciano
2017
Abstract
For any pair of categories (C, K) enriched over the category Gpd of groupoids, it is possible to define a strong shape category SSh(C, K) in such a way that, for C the category of topological spaces and K its full subcategory of spaces having the homotopy type of absolute neighborhoods retracts for metric spaces, one obtains the strong shape category SSh(Top) , as defined by Mardešić. We also introduce a new category SSK with the same objects as C and morphisms given by suitable pseudo-natural transformations into the category of groupoids. The main result is then that such a category SSK is isomorphic to the strong shape category SSh(C, K) , when C is also a proper model category.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.