Comments for Annoying Precision
https://qchu.wordpress.com
"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 HalmosSun, 03 Sep 2017 04:14:26 +0000hourly1http://wordpress.com/Comment on Groupoid cardinality by The Groupoid Cardinality of Finite Semi-Simple Algebras | The Germs of Generality
https://qchu.wordpress.com/2012/11/08/groupoid-cardinality/#comment-7711
Sun, 03 Sep 2017 04:14:26 +0000http://qchu.wordpress.com/?p=11651#comment-7711[…] It is important to count only one object from each isomorphism class since we want the notion of groupoid cardinality to be invariant under equivalences of groupoids (in the sense of category theory) and every category is equivalent to it’s skeleton. For further motivation for the idea of a groupoid cardinality, see Qiaochu Yuan’s post on them […]
]]>Comment on Split epimorphisms and split monomorphisms by Qiaochu Yuan
https://qchu.wordpress.com/2012/10/01/split-epimorphisms-and-split-monomorphisms/#comment-7674
Sun, 27 Aug 2017 19:11:16 +0000http://qchu.wordpress.com/?p=10955#comment-7674In , the epimorphisms are precisely the surjective maps, and takes values in .
]]>Comment on Split epimorphisms and split monomorphisms by adi
https://qchu.wordpress.com/2012/10/01/split-epimorphisms-and-split-monomorphisms/#comment-7673
Sun, 27 Aug 2017 18:26:04 +0000http://qchu.wordpress.com/?p=10955#comment-7673Sorry, I want to clarify the proof of (2) => (3) in the definition-proposition of split-epi. In general epi not necessarily surjective right? meanwhile in the proof we need the surjectivity of F(f) for the functor F=Hom(-,c). Do I miss something?
]]>Comment on About by elienasrallah
https://qchu.wordpress.com/about/#comment-7649
Mon, 21 Aug 2017 13:30:24 +0000#comment-7649Hi. I would like to know how do you make LaTex work in a post excerpt on your homepage. I had to put the whole post to make Latex work; if I chose to put an excerpt, Latex would not parse! Thank you
]]>Comment on Hypersurfaces, 4-manifolds, and characteristic classes by Interested Amateur
https://qchu.wordpress.com/2014/06/16/hypersurfaces-4-manifolds-and-characteristic-classes/#comment-7594
Thu, 10 Aug 2017 14:49:47 +0000http://qchu.wordpress.com/?p=15433#comment-7594It appears that I forgot to use the statement for the homology in lower-than-middle degree. That’ll do it!
]]>Comment on Hypersurfaces, 4-manifolds, and characteristic classes by Interested Amateur
https://qchu.wordpress.com/2014/06/16/hypersurfaces-4-manifolds-and-characteristic-classes/#comment-7593
Thu, 10 Aug 2017 10:15:11 +0000http://qchu.wordpress.com/?p=15433#comment-7593Looking at your computation at the start of “most of the cohomology”, it is not quite clear to me how Poincaré duality tells you all of the cohomology groups above middle degree. As far as I can tell, you need the universal coefficients theorem (since the duality gets you to homology instead of cohomology). This works fine for every degree except the one right above middle degree (i.e. degree n in your notation). Here, there might a priori be torsion coming from the middle-degree (co)homology. I’m probably missing something stupid, but I’m wondering how this is resolved: Would you indulge me?
]]>Comment on Maximum entropy from Bayes’ theorem by waltonmath
https://qchu.wordpress.com/2016/03/06/maximum-entropy-from-bayes-theorem/#comment-7436
Wed, 28 Jun 2017 21:38:05 +0000http://qchu.wordpress.com/?p=23466#comment-7436You mentioned the traditional statement of Bayes’ Theorem being annoying to remember. The following mnemonic is useful for me:

P(A, B) = P(A, B)
P(A)P(B|A) = P(B)P(A|B)
P(B|A) = P(B)P(A|B)/P(A)

]]>Comment on Finite index subgroups of the modular group by Richard Stanley
https://qchu.wordpress.com/2015/11/15/finite-index-subgroups-of-the-modular-group/#comment-7354
Tue, 13 Jun 2017 01:05:17 +0000http://qchu.wordpress.com/?p=20404#comment-7354See “Enumerative Combinatorics,” vol. 2, Exercise 5.13.
]]>Comment on The adjoint functor theorem for posets by Dean
https://qchu.wordpress.com/2010/10/22/the-adjoint-functor-theorem-for-posets/#comment-7183
Thu, 11 May 2017 11:04:53 +0000http://qchu.wordpress.com/?p=5627#comment-7183Ok thanks
]]>Comment on The adjoint functor theorem for posets by Qiaochu Yuan
https://qchu.wordpress.com/2010/10/22/the-adjoint-functor-theorem-for-posets/#comment-7179
Thu, 11 May 2017 07:17:46 +0000http://qchu.wordpress.com/?p=5627#comment-7179The hypotheses are stated in the post: I need that has, and preserves, small limits. This implies that is a complete lattice (by the adjoint functor theorem!) but in principle needn’t be, although in practice it probably will be.
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