Sunto
In queste note, consideriamo versioni diverse dei funtori di coinduzione tra categorie di comoduli per coanelli indotti da un morfismo di coanelli. In particolare introduciamo una nuova versione del funtore di coinduzione nel caso di coanellilocalmente proiettivi come composizione di opportuni funtori «Traccia» e «Hom» e mostriamo come derivarlo da un piùgenerale funtore di coinduzione tra categorie di tipo σ[M]. In casi particolari (es. il morfismo di coanelli è parte di un morfismo che misura glia-accoppiamenti oppure i coanelli hanno lo stesso anello base), dimostriamo che una versione del nostro funtore è isomorfo all'usuale funtore di coinduzione ottenuto tramite il prodotto cotensoriale. I risultati di queste note generalizzano precedenti risultati dell'autore sui funtori di coinduzione tra categorie di comoduli per coalgebre su anelli base commutativi.
Abstract
In this note we consider different versions of coinduction functors between categories of comodules for corings induced by a morphism of corings. In particular we introduce a new version of the coinduction functor in the case oflocally projective corings as a composition of suitable “Trace” and “Hom” functors and show how to derive it from a moregeneral coinduction functor between categories of type σ[M]. In special cases (e.g. the corings morphism is part of a morphism of measuringa-pairings or the corings have the same base ring), a version of our functor is shown to be isomorphic to the usual coinduction functor obtained by means of the cotensor product. Our results in this note generalize previous results of the author on coinduction functors between categories of comodules for coalgebras over commutative base rings.
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Abuhlail, J.Y. A note on coinduction functors between categories of comodules for corings. Ann. Univ. Ferrara 51, 151–172 (2005). https://doi.org/10.1007/BF02824828
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DOI: https://doi.org/10.1007/BF02824828