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diff --git a/posts/blog-architecture-2.md b/posts/blog-architecture-2.md
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-% More on the Architecture of math.kleen.org
-
-It's been more than a month since the last post here. Sorry about that. But I
-have now implemented a nice and fancy new feature for math.kleen.org, namely
-theorem environments:
-
-<thm>
-This could be your theorem here!
-</thm>
-
-<cor>
-Some theorems come with corollaries.
-</cor>
-
-How these work ties in quite well with describing how LaTeX formulas are
-converted to SVG for display in your browser. For example:
-$$
-\int_{\partial M}\omega = \int_M\dd\omega
-$$
-
-Both these features are accomplished via extensive processing with
-[Pandoc](http://en.wikipedia.org/wiki/Pandoc). For converting LaTeX snippets
-into SVG, I have a little Haskell program that takes Pandocs native format,
-extracts all math snippets and compiles them with latex and dvisvgm. This
-program sits in the build subdirectory in
-<https://github.com/vkleen/math.kleen.org>.
-
-For the theorem environment I patched the Markdown reader to convert mock HTML
-tags like `<thm>` or `<cor>` into proper HTML. That way I can also retain the
-possibility of converting posts into LaTeX and make PDFs out of them.
-
-I'm not sure whether I will continue documenting this software like that. But if
-I ever write a redo replacement there will probably a few posts on the process.
diff --git a/posts/blog-architecture.md b/posts/blog-architecture.md
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-% An Outline of the Architecture of math.kleen.org
-
-The main idea behind this system is that my site is supposed to consist of
-*posts* which are organized into *lists of posts*. This mapping is not assumed
-to be injective, i.e. a post may be a member of many lists. In fact, this is how
-the list [All Posts](/lists/zz_all.html) is made: every post is supposed to be
-linked into it.
-
-To keep order in this mess of data, I have decided to map it into the file
-system. I have a folder `posts` which contains all posts and a folder `lists`
-with all the lists. Every list is a folder with symbolic links to posts:
-
-    blog
-    ├── lists
-    │   ├── all
-    │   │   ├── 001 -> ../../posts/hello-world.md
-    │   │   └── title
-    │   ├── blog
-    │   │   └── title
-    └── posts
-        └── hello-world.md
-
-As you can see, I have added a special file to each list folder named `title`
-which contains the title of the list (as you might have guessed).
-
-Posts are written as [Markdown](http://en.wikipedia.org/wiki/Markdown) files and
-converted to HTML with [Pandoc](http://en.wikipedia.org/wiki/Pandoc). Pandoc
-handles this conversion almost perfectly, but I had one small issue with
-it. Namely, I want to be able to write mathematics and hence translate
-TeX--snippets into something that your browser can display.
-
-Pandoc has several builtin methods to do this, but most of them either rely on a
-specialised TeX--parser or JavaScript. Both were deemed too ugly to use. So I
-wrote a filter around Pandoc to extract TeX-snippets and compile them with my
-regular LaTeX distribution into SVG. This seems to work quite nicely.
-
-The next issue was keeping this mess of posts and lists and Markdown files under
-control. Traditionally, I would have used a Makefile for that but I wanted
-something a little nicer this time. I turned to an old idea of
-[Dan Bernstein's](http://cr.yp.to/djb.html):
-[Redo](http://cr.yp.to/redo.html). There are several implementations of Redo out
-there; eventually I plan to write my own, just as practice. For now, I use a
-very minimal implementation in shell script from
-<https://github.com/apenwarr/redo>.
-
-More on how exactly the conversion from Markdown to HTML and all the associated
-ecosystem works will appear in a later post.
diff --git a/posts/hello-world.md b/posts/hello-world.md
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-% Hello, World!
-
-This is the inaugural post for this site. This "blog" is supposed to become
-populated by a variety of posts pertaining to my research at USC, to personal
-projects and (mathematicians, look away!) its own architecture.
-
-At the moment, I don't have much content; but hopefully this will change in due
-time. In the first few posts, I think I will describe the custom software that I
-put together to make this website happen; mostly for my benefit, so I have
-documentation to fall back on once things break.
-
-This is all I have to say right now. Carry on!
diff --git a/posts/torsors.md b/posts/torsors.md
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-% Torsors and Their Classification I
-
-# Torsors in Grothendieck Toposes #
-
-Let $\ca C$ be some Grothendieck topos, that is a category of sheaves on some
-Grothendieck topology. This text will look at some properties of *torsors* in
-$\ca C$ and how they might be classified using cohomology and homotopy
-theory. For this we will first need to define group objects. Torsors will then
-be associated to those.
-
-<defn> A *group object* in a category $\ca C$ is an object $G\in\ca C$ such that
-the associated Yoneda functor $\hom(\_,G)\colon \op{\ca C}\to\Set$ actually
-takes values in the category $\Grp$ of groups.  </defn>
-
-A trivial kind of example would be just a group considered as an object in
-$\Set$. A more involved example would be a *group scheme* $G$ over some base
-$S$. Such a thing is essentially defined as a group object in the category
-$\sch[S]$. If we have any subcanonical topology on $\sch[S]$, then $G$ defines a
-sheaf on the associated site and we obtain in this way a group object in the
-corresponding topos on $S$.
-
-Let's now assume we have a group object $G$ in a Grothendieck topos $\ca
-C$. Then we can define torsors over $G$ as follows:
-
-<defn> A *trivial $G$--torsor* is an object $X$ with a left $G$--action which is
-isomorphic to $G$ itself with the action given by left multiplication.  </defn>
-
-<defn> A *$G$--torsor* is an object $X\in\ca C$ with a left $G$--action which is
-locally isomorphic to a trivial torsor; that is, there is an epimorphism $U\to
-*$ such that $U\times X$ is a trivial torsor in $\ca C/U$ over $U \times G$.
-</defn>
-
-I want to show that for any $G$--torsor $X$ according to this definition the
-left action of $G$ on $X$ is free and transitive, that is the map
-$$ f\colon G\times X \to X\times X $$
-given (on generalized elements) by $f(g, x) = (gx, x)$ is an isomorphism. This
-is going to be some relatively elementary category theory but I think it's worth
-writing it up. First a few facts about isomorphisms in toposes, they can be
-found for example in Sheaves in Geometry and Logic.[^1]
-
-<lem>
-Epimorphisms in a topos are stable under pullback.
-</lem>
-<lem>
-In a topos every morphism $f\colon X\to Y$ has a functorial factorization $f =
-m\circ e$ with $m$ a monomorphism and $e$ and epimorphism.
-</lem>
-<lem>
-A morphism $f$ is an isomorphism if and only if $f$ is both monic and epic.
-</lem>
-
-Now, let $f\colon A\to B$ be a *local monomorphism*, i.e. there is an epimorphism
-$U\to *$ such that the pullback $f\times U$ of $f$ to $U$ is a
-monomorphism. Then, since epimorphisms are stable under pullback, it follows that
-in the commutative square
-$$
-\begin{tikzcd}
-A\times U \ar[into, r, "f\times U"] \ar[onto, d] & B\times U \ar[onto, d] \\
-A \ar[r, "f"'] & B
-\end{tikzcd}
-$$
-both vertical maps are epimorphisms. Now let $\varphi,\psi\colon T\to A$ be a pair of morphisms
-such that $f\varphi = f\psi$. Then, denoting by $\varphi_U$ and $\psi_U$ the
-pullbacks to $U$, we have $f_U\varphi_U = f_U\psi_U$. but $f_U$ is a
-monomorphism by assumption, so $\varphi_U = \psi_U$. So we have a commutative
-diagram
-$$
-\begin{tikzcd}
-T\times U \ar[r, "\varphi_U = \psi_U"] \ar[onto, d] & A\times U \ar[onto, d] \\
-T \ar[r, "\varphi", shift left] \ar[r, "\psi"', shift right] & A
-\end{tikzcd}
-$$
-in which the vertical maps are epimorphisms. It follows that $\varphi =
-\psi$.
-
-Now, if $f$ is a local epimorphism, then again we have the diagram
-$$
-\begin{tikzcd}
-A\times U \ar[onto, r, "f\times U"] \ar[onto, d] & B\times U \ar[onto, d] \\
-A \ar[r, "f"'] & B
-\end{tikzcd}
-$$
-and it is immediate that $f$ is an epimorphism. In summary:
-
-<prop>
-In a topos, any local epimorphism is an epimorphism, any local monomorphism is a
-monomorphism, and any local isomorphism is an isomorphism.
-</prop>
-
-Now, let's check that $G$--torsors $X$ as defined above are free and
-transitive. Take an epimorphism $U\onto *$ such that $X\times U$ is trivial in
-$\ca C/U$. The action of $G$ on itself by left multiplication is plainly free
-and transitive, so in $\ca C/U$ we have the isomorphism
-$$(G\times U)\times_U (X\times U) \iso (X\times U)
-\times_U (X\times U)$$
-and $(G\times U)\times_U(X\times U) = (G\times X)\times U$ and $(X\times
-U)\times_U (X\times U) = (X\times X)\times U$ because pullback preserves products. So, $G\times X\to
-X\times X$ is a local isomorphism, hence an isomorphism.
-
-[^1]: Saunders Mac Lane, Ieke Moerdijk. Sheaves in geometry and logic. Springer, 1994. ISBN: 0-387-97710-4