Comments on: Projective objects
https://qchu.wordpress.com/2015/03/28/projective-objects/
"A good stock of examples, as large as possible, is indispensable for a thorough understanding of any concept, and when I want to learn something new, I make it my first job to build one." - Paul HalmosFri, 19 Feb 2016 02:48:33 +0000
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By: Qiaochu Yuan
https://qchu.wordpress.com/2015/03/28/projective-objects/#comment-6182
Fri, 19 Feb 2016 02:35:04 +0000http://qchu.wordpress.com/?p=17224#comment-6182In reply to Arpon.

Oops, you’re completely right; I never show that implies anything. Thanks for the correction!

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By: Arpon
https://qchu.wordpress.com/2015/03/28/projective-objects/#comment-6181
Fri, 19 Feb 2016 00:52:31 +0000http://qchu.wordpress.com/?p=17224#comment-6181You claim that if a linear functor between abelian categories preserves epis then it’s right exact, but it’s not proven by the implications given in the proof. And it seems to be false in general (e.g. http://math.stackexchange.com/a/406602/5226), though of course it’s equivalent for left-exact functors like Hom.
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By: Generators | Annoying Precision
https://qchu.wordpress.com/2015/03/28/projective-objects/#comment-5098
Mon, 18 May 2015 03:54:28 +0000http://qchu.wordpress.com/?p=17224#comment-5098[…] due to Gabriel characterizing categories of modules as cocomplete abelian categories with a compact projective generator, where “generator” meant “every object is a colimit of finite direct […]
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By: Tiny objects | Annoying Precision
https://qchu.wordpress.com/2015/03/28/projective-objects/#comment-5085
Thu, 07 May 2015 21:26:10 +0000http://qchu.wordpress.com/?p=17224#comment-5085[…] projective: preserves epimorphisms (since it preserves […]
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By: Compact objects | Annoying Precision
https://qchu.wordpress.com/2015/03/28/projective-objects/#comment-5069
Sun, 26 Apr 2015 04:36:36 +0000http://qchu.wordpress.com/?p=17224#comment-5069[…] « Projective objects […]
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