Pure Direct Projective Objects in Grothendieck Categories
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2022xmlui.dri2xhtml.METS-1.0.item-emb
Acik erisim
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We study generalizations of the concept of direct-projectivity (respectively
pure-direct-projectivity) from module categories to abelian categories (respectively
Grothendieck categories). We examine for which categories or under what conditions
direct-projective objects are projective. Also we examine for which categories or under what
conditions pure-direct-projective objects are projective, quasi-projective, pure-projective,
flat or direct-projective. We investigate classes all of whose objects are direct-projective
(respectively pure-direct-projective). We also give applications of some results to module
categories and comodule categories.
