Injectivity paucity in AB5 categories of oversize chains
Abstract
We construct examples of abelian categories with no non-zero injective (or projective) objects satisfying Grothendieck's AB5 condition. The procedure combines Rickard's examples of AB5 categories without products but some non-trivial injectives (also addressing an apparent gap in the literature) with a 2-functorial construct attaching to any category C that of C-objects equipped with set-indexed families of endomorphisms.
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