Thesis: Added references (+typo, todos)

make

@@ -16,6 +16,9 @@ Symbols)	pdflatex "../thesis/symbols.tex" || exit 1
 		scp moerman@stitch.science.ru.nl:~/symbols.svg ../
 		;;
 Thesis)		pdflatex "../thesis/DoldKan.tex" || exit 1
+		cp "../thesis/references.bib" ./ || exit 1
+		bibtex DoldKan                   || exit 1
+		pdflatex "../thesis/DoldKan.tex" || exit 1
 		pdflatex "../thesis/DoldKan.tex" || exit 1
 		mv DoldKan.pdf ../
 		;;

thesis/2_ChainComplexes.tex

@@ -84,6 +84,7 @@ Note that we will often drop the indices of the boundary morphisms, since it is
 	$$ H_n(f \circ g)([x]) = [f_n(g_n(x))] = H_n(f)([g_n(x)]) = H_n(f) \circ H_n(g) ([x]). $$
 \end{proof}
 
+\todo{Ch: Note that $\Ch{\Ab}$ is an ab. cat. At least show functoriality $\Hom{\Ch{\Ab}}{-}{-}$}
 \todo{CC: What to do with the example...}
 \subsection{The singular chain complex}
 In order to see why we are interested in the construction of homology groups, we will look at an example from algebraic topology. We will see that homology gives a nice invariant for spaces. So we will form a chain complex from a topological space $X$. In order to do so, we first need some more notions.
@@ -133,8 +134,6 @@ This might seem a bit complicated, but we can pictures this in an intuitive way,
 	\caption{The boundary of a 2-simplex, and a boundary of a 1-simple}
 	\label{fig:singular_chaincomplex}
 \end{figure}
-\todo{CC: update picture}
 
-\todo{Ch: Proposition: $C(X) \in \Ch{\cat{Ab}}$}
+\todo{Ch: Proposition: $C(X) \in \Ch{\cat{Ab}}$?}
 \todo{Ch: Example homology of some space}
-\todo{Ch: Show that $\Ch{\Ab}$ is an ab. cat. At least show functoriality $\Hom{\Ch{\Ab}}{-}{-}$}

thesis/DoldKan.tex

@@ -1,4 +1,4 @@
-\documentclass[12pt]{amsproc}
+\documentclass[11pt]{amsproc}
 
 % a la fullpage
 \usepackage{geometry}
@@ -29,13 +29,13 @@
 \maketitle
 
 \section*{Introduction}
-In this thesis we will look at a correspondence which was discovered by A. Dold and D. Kan independently, hence it is called the \emph{Dold-Kan correspondence}. Abstractly it is the following equivalence of categories:
+In this thesis we will look at a correspondence which was discovered by A. Dold \cite{dold} and D. Kan \cite{kan} independently, hence it is called the \emph{Dold-Kan correspondence}. Abstractly it is the following equivalence of categories:
 $$ \Ch{\Ab} \simeq \sAb $$
 It is interesting because objects on the left hand side are considered to be algebraic of nature, whereas objects on the right are more topological. Objects of either of these categories have important invariants. A more refined statement of this equivalence tells us that there is an isomorphism between homology groups (on the left hand side) and homotopy groups (on the right hand side). A bit more precise:
 $$ \pi_n(A) \iso H_n(N(A)) \text{ for all } n \in \N $$
 where $N: \sAb \to \Ch{\Ab}$ is one half of the equivalence.
 
-In the first section some definitions from category theory are given, because we will need them later on. Then in the second section we will discuss the first category involved in the correspondence, $\Ch{\Ab}$, the category of chain complexes. The third section then continues with the second category involved, $\sAb$, especially for this section we will need category theory. Then we will look at the coorespondence itself.
+In the first section some definitions from category theory are given, because we will need them later on. Then in the second section we will discuss the first category involved in the correspondence, $\Ch{\Ab}$, the category of chain complexes. The third section then continues with the second category involved, $\sAb$, especially for this section we will need category theory. Then we will look at the correspondence itself.
 
 \newpage
 \input{../thesis/1_CategoryTheory}
@@ -57,7 +57,8 @@ In the first section some definitions from category theory are given, because we
 
 \newpage
 \listoftodos
-% \nocite{*}
-% \bibliographystyle{alpha}
-% \bibliography{references}	
+
+\nocite{*}
+\bibliographystyle{alpha}
+\bibliography{references}	
 \end{document}

thesis/references.bib

@@ -0,0 +1,67 @@
+@article{friedman,
+	title={An elementary illustrated introduction to simplicial sets},
+	author={Friedman, Greg},
+	journal={arXiv preprint arXiv:0809.4221v4},
+	year={2011}
+}
+
+@book{lamotke,
+	title={Semisimpliziale algebraische Topologie},
+	author={Lamotke, Klaus},
+	volume={147},
+	year={1968},
+	publisher={Springer-Verlag}
+}
+
+@article{kan,
+	title={Functors involving css complexes},
+	author={Kan, Daniel M},
+	journal={Transactions of the American Mathematical Society},
+	volume={87},
+	number={2},
+	pages={330--346},
+	year={1958},
+	publisher={JSTOR}
+}
+
+@article{dold,
+	title={Homology of symmetric products and other functors of complexes},
+	author={Dold, Albrecht},
+	journal={The Annals of Mathematics},
+	volume={68},
+	number={1},
+	pages={54--80},
+	year={1958},
+	publisher={JSTOR}
+}
+
+@book{weibel,
+	title={An introduction to homological algebra},
+	author={Weibel, Charles A},
+	volume={38},
+	year={1995},
+	publisher={Cambridge university press}
+}
+
+@book{rotman,
+	title={An introduction to homological algebra},
+	author={Rotman, Joseph J},
+	year={2009},
+	publisher={Springer Science+ Business Media}
+}
+
+@book{awodey,
+	title={Category theory},
+	author={Awodey, Steve},
+	volume={52},
+	year={2010},
+	publisher={Oxford University Press}
+}
+
+@article{maclane,
+	title={Category theory for the working mathematician},
+	author={Mac Lane, Saunders},
+	journal={Graduate Texts in Mathematics},
+	volume={5},
+	year={1971}
+}