\documentclass[12pt,a4paper]{report} \usepackage[unicode,psdextra,final]{hyperref} \usepackage{mystyle} \iffalse %%% Watermark \usepackage{draftwatermark} \SetWatermarkText{DRAFT} \SetWatermarkScale{2} %%% \fi %%% For line numbering (used for proodreading purposes) %% \usepackage[pagewise,displaymath, mathlines]{lineno} %% \linenumbers \title{Homology of strict $\omega$-categories} \author{Léonard Guetta} \begin{document} \maketitle \abstract{In this dissertation, we study the homology of strict $\oo$\nbd{}categories. More precisely, we intend to compare the ``classical'' homology of an $\oo$\nbd{}category (defined as the homology of its Street nerve) with its polygraphic homology. Along the way, we prove several important results concerning free strict $\oo$\nbd{}categories on polygraphs (also known as computads) and concerning the homotopy theory of strict $\oo$\nbd{}categories. } \tableofcontents \include{introduction} \include{omegacat} \include{homtheo} \include{hmtpy} \include{hmlgy} \include{contractible} \include{2cat} \addcontentsline{toc}{chapter}{Bibliography} \bibliographystyle{alpha} \bibliography{memoire} \end{document} %%% Local Variables: %%% mode: latex %%% TeX-master: t %%% End: