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The Functor of Points | a fully faithful embedding | functorofpoints.wordpress.com Reviews
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a fully faithful embedding (by Dan Bragg)
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July | 2015 | The Functor of Points
https://functorofpoints.wordpress.com/2015/07
The Functor of Points. A fully faithful embedding. Monthly Archives: July 2015. Posted by Dan Bragg. On July 5, 2015. By Qiaochu Yuan. Here is the definition. Commutes with filtered colimits. To be precise, what we mean by this is that for any filtering system. Before we do some examples, lets give a general argument that will sometimes allow us to characterize all of the compact objects in a category. We will say that a set. Of objects in a category. If every object of. Is a colimit of objects in. Are e...
Sheaffy Matrix Algebra and the Skolem-Noether Theorem | The Functor of Points
https://functorofpoints.wordpress.com/2015/08/01/sheaffy-matrix-algebra-and-the-skolem-noether-theorem
The Functor of Points. A fully faithful embedding. Sheaffy Matrix Algebra and the Skolem-Noether Theorem. Posted by Dan Bragg. On August 1, 2015. Or more generally a ring), we can form the matrix ring. Is functorial. In fact, it is even better than that: it is a sheaf! For the rest of this post, we will work in the Zariski topology, although it turns out that the whole discussion remains valid in the etale or fppf topologies). One consequence of this is that given a scheme. By gluing together the algebras.
August | 2015 | The Functor of Points
https://functorofpoints.wordpress.com/2015/08
The Functor of Points. A fully faithful embedding. Monthly Archives: August 2015. Morita Theory and Reconstruction. Posted by Dan Bragg. On August 18, 2015. Given a “non-linear” object it is often useful to study various “linear” objects attached to it. For instance, given a ring. We get the category of. Act on an abelian group. Given a group. We get linear representations of. Act on vector spaces. Given a space. We can study vector bundles on. Or more generally, sheaves of abelian groups on. Modules....
Categorical Compactness I | The Functor of Points
https://functorofpoints.wordpress.com/2015/07/05/hello-world/comment-page-1
The Functor of Points. A fully faithful embedding. Posted by Dan Bragg. On July 5, 2015. By Qiaochu Yuan. Here is the definition. Commutes with filtered colimits. To be precise, what we mean by this is that for any filtering system. Before we do some examples, lets give a general argument that will sometimes allow us to characterize all of the compact objects in a category. We will say that a set. Of objects in a category. If every object of. Is a colimit of objects in. That is, every object in. Are exac...
Categorical Compactness I | The Functor of Points
https://functorofpoints.wordpress.com/2015/07/05/hello-world
The Functor of Points. A fully faithful embedding. Posted by Dan Bragg. On July 5, 2015. By Qiaochu Yuan. Here is the definition. Commutes with filtered colimits. To be precise, what we mean by this is that for any filtering system. Before we do some examples, lets give a general argument that will sometimes allow us to characterize all of the compact objects in a category. We will say that a set. Of objects in a category. If every object of. Is a colimit of objects in. That is, every object in. Are exac...
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functor
Computer art and things that are not computer or art. This was posted 1 day ago. It has 14 notes. I wrote a little assembler/disassembler/emulator for a virtual MIPS-like CPU. The code is both pulic and horrific at github.com/reuk/beatcomputer. The plan is to turn it into a low-level environment for music sequencing - a bit like IXI-lang, but (much) more computational. Heavily inspired by the Betablocker project and the game TIS-100. This was posted 1 month ago. It has 33 notes. It’s capable of doi...
Phil Freeman
I am a full-stack developer working with functional programming languages, based in Los Angeles, CA. I enjoy applying the techniques of pure functional programming to real-world problems. Find me on Twitter.
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The Functor of Points | a fully faithful embedding
The Functor of Points. A fully faithful embedding. Posted by Dan Bragg. On August 3, 2015. We defined an abstract finiteness condition called compactness. We also proved, among other things, that the compact objects in module categories were precisely the finitely-presented modules. Given that we have a nice characterization of compact objects in. Mod, an obvious question (for the right sort of person) is to ask what are the compact objects in. Under mild hypothesis on. It is known that. Using the fact t...
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