Comments on: My Favorite Random Fact About Abelian Categories http://cornellmath.wordpress.com/2007/07/20/my-favorite-random-fact-about-abelian-categories/ Geometry, Topology, Categories, Groups, Physics, . . . Everything Sat, 19 Jul 2008 10:31:44 +0000 http://wordpress.org/?v=MU By: icecube http://cornellmath.wordpress.com/2007/07/20/my-favorite-random-fact-about-abelian-categories/#comment-81 icecube Mon, 23 Jul 2007 16:34:40 +0000 http://cornellmath.wordpress.com/2007/07/20/my-favorite-random-fact-about-abelian-categories/#comment-81 Oh that's also my favourite fact about abelian categories! I don't, however, know much more personally about them. Oh that’s also my favourite fact about abelian categories! I don’t, however, know much more personally about them.

]]> By: Ars Mathematica » Blog Archive » Secret of Blogging about Everything http://cornellmath.wordpress.com/2007/07/20/my-favorite-random-fact-about-abelian-categories/#comment-72 Ars Mathematica » Blog Archive » Secret of Blogging about Everything Sun, 22 Jul 2007 05:59:08 +0000 http://cornellmath.wordpress.com/2007/07/20/my-favorite-random-fact-about-abelian-categories/#comment-72 [...] both cover a broad range of advanced topics. Enjoy them while you can — as you can see here open hostilities between the two are about to break [...] [...] both cover a broad range of advanced topics. Enjoy them while you can — as you can see here open hostilities between the two are about to break [...]

]]> By: John Armstrong http://cornellmath.wordpress.com/2007/07/20/my-favorite-random-fact-about-abelian-categories/#comment-70 John Armstrong Sat, 21 Jul 2007 02:12:35 +0000 http://cornellmath.wordpress.com/2007/07/20/my-favorite-random-fact-about-abelian-categories/#comment-70 I'm not so sure this is really "secret". There are a lot of these sorts of enriched categories. Let's say you have a category with "zero morphisms". That is, for every pair of objects $latex A$ and $latex B$ there's a morphism $latex 0:A\rightarrow B$ so that $latex 0\circ f$ and $latex g\circ0$ are the appropriate zero morphisms. This is "secretly" the same thing as a category enriched over $latex \mathbf{pSet}$ -- the category of pointed sets. We can slip back and forth between seeing it as a category that satisfies certain properties or an enriched category. I’m not so sure this is really “secret”. There are a lot of these sorts of enriched categories.

Let’s say you have a category with “zero morphisms”. That is, for every pair of objects A and B there’s a morphism 0:A\rightarrow B so that 0\circ f and g\circ0 are the appropriate zero morphisms. This is “secretly” the same thing as a category enriched over \mathbf{pSet} — the category of pointed sets. We can slip back and forth between seeing it as a category that satisfies certain properties or an enriched category.

]]> By: A.J. Tolland http://cornellmath.wordpress.com/2007/07/20/my-favorite-random-fact-about-abelian-categories/#comment-69 A.J. Tolland Sat, 21 Jul 2007 01:26:36 +0000 http://cornellmath.wordpress.com/2007/07/20/my-favorite-random-fact-about-abelian-categories/#comment-69 Coincidentally, I'll be keeping an eye on you^H^H^H^H visiting the library at MSRI next week. Coincidentally, I’ll be keeping an eye on you^H^H^H^H visiting the library at MSRI next week.

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