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Morita equivalence and the bicategory of bimodules | Annoying Precision
https://qchu.wordpress.com/2012/02/16/morita-equivalence-and-the-bicategory-of-bimodules
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 Halmos. Laquo; Centers, 2-categories, and the Eckmann-Hilton argument. Morita equivalence and the bicategory of bimodules. February 16, 2012 by Qiaochu Yuan. In the previous post. We learned that it is possible to recover the center. Of left modules (as an. Are said to be Morita equivalent. In other words, it is i...
qchu.wordpress.com
Reading Recommendations | Annoying Precision
https://qchu.wordpress.com/reading-recommendations
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 Halmos. The following list is mostly intended for undergraduates. The recommendations here generally emphasize clarity of exposition over technical detail. Algebra and Number Theory. Fearless Symmetry: Exposing the Hidden Patterns of Numbers. On Quaternions and Octonions. Primes of the Form. The Shape of Space.
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Compact objects | Annoying Precision
https://qchu.wordpress.com/2015/04/25/compact-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 Halmos. Laquo; Projective objects. April 25, 2015 by Qiaochu Yuan. Is a noncommutative ring, then Morita theory. Cannot in general be recovered from its category. Of modules; that is, there can be a ring. Or equivalently on a choice of forgetful functor. Be a category which has filtered colimits. Maps out of a fin...
qchu.wordpress.com
The Picard groups | Annoying Precision
https://qchu.wordpress.com/2014/10/19/the-picard-groups
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 Halmos. Laquo; Five proofs that the Euler characteristic of a closed orientable surface is even. October 19, 2014 by Qiaochu Yuan. Be a commutative ring. From. We can construct the category. Modules, which becomes a symmetric monoidal category when equipped with the tensor product of. Such that the tensor product.
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Five proofs that the Euler characteristic of a closed orientable surface is even | Annoying Precision
https://qchu.wordpress.com/2014/10/14/five-proofs-that-the-euler-characteristic-of-a-closed-orientable-surface-is-even
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 Halmos. Laquo; Hypersurfaces, 4-manifolds, and characteristic classes. Five proofs that the Euler characteristic of a closed orientable surface is even. October 14, 2014 by Qiaochu Yuan. Be a closed orientable surface of genus. Below we will occasionally write. Omitting the genus.) Then its Euler characteristic.
qchu.wordpress.com
Projective objects | Annoying Precision
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 Halmos. Laquo; Topological Diophantine equations. March 28, 2015 by Qiaochu Yuan. The goal of this post is to summarize some more-or-less standard facts about projective objects. Here is some slightly nonstandard terminology: we’ll call an. Enriched category a linear category. A commutative ring) is a. If it prese...
qchu.wordpress.com
Generators | Annoying Precision
https://qchu.wordpress.com/2015/05/17/generators
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 Halmos. Laquo; Tiny objects. Dualizable objects (and morphisms). May 17, 2015 by Qiaochu Yuan. We proved a theorem due to Gabriel characterizing categories of modules as cocomplete abelian categories with a compact. Satisfies the first condition but not the second. More generally, as Mike Shulman explains here.
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Qiaochu Yuan | Annoying Precision
https://qchu.wordpress.com/author/qchu
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 Halmos. Http:/ math.berkeley.edu/ qchu/. Posts by Qiaochu Yuan:. May 31, 2016. May 26, 2016. What’s a fire, and why does it – what’s the word – burn? May 23, 2016. More on partition asymptotics. May 20, 2016. The man who knew partition asymptotics. May 8, 2016. March 27, 2016. March 20, 2016. Older Posts ».
qchu.wordpress.com
Tiny objects | Annoying Precision
https://qchu.wordpress.com/2015/05/07/tiny-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 Halmos. Laquo; Compact objects. May 7, 2015 by Qiaochu Yuan. The starting observation of Morita theory. Is that the abelian category. Of (right) modules over a (not necessarily commutative) ring. Does not uniquely determine. Since for example we always have Morita equivalences. Is equivalent to isolating the module.
