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\begin{document}

\begin{titlepage}
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   {
   \scshape{\textbf{Université de Paris}} \par}
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 {\large École de Sciences Mathématiques Paris Centre (ED 386)}
 
 {Institut de Recherche Fondamentale en Informatique (IRIF)}
 %{\large Institut de Recherche Fondamentale en Informatique (IRIF)}

 \vspace*{0.25cm}

 {\Large
   \scshape
   \textbf{Thèse de doctorat en Mathématiques}}

      {\large Dirigée par François Métayer \\
        et par Clemens Berger \par}

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      \centering
        {\Huge \scshape \textbf{Homology of strict $\omega$-categories}\par}

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        {\Large
          
        \textbf{par Léonard Guetta}}





   \vfill 
   {\slshape Présentée et soutenue publiquement le 15 janvier 2021 \\
     devant un jury composé de : \par}
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    \begin{tabular}{ll}
      \textbf{M. Benoît Fresse} (Prof., Université de Lille) & Rapporteur \\
      \textbf{M. Richard Garner} (Senior Lecturer, University Maquarie) & Rapporteur \\
      \textbf{Mme Eugenia Cheng} (Prof., School of the Art Institute) & Examinatrice \\
      \textbf{M. Carlos Simpson} (DR CNRS, Université de Paris) & Examinateur \\
      \textbf{M. Samuel Mimram} (Prof., École Polytechnique) & Examinateur \\
      \textbf{M. Georges Maltsiniotis} (DR CNRS, Université de Nice) & Examinateur \\
      \textbf{M. François Métayer} (MCF, Université de Paris Nanterre) & Directeur de Thèse \\
      \textbf{M. Clemens Berger} (MCF, Université de Nice) & Co--directeur de Thèse \\
      \textbf{M. Dimitri Ara} (MCF, Université Aix-Marseille) & Membre invité 
      \end{tabular}
     
            
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\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{introduction_fr}
\include{omegacat}
\include{homtheo}
\include{hmtpy}
\include{hmlgy}
\include{contractible}
\include{2cat}

\addcontentsline{toc}{chapter}{Bibliography}
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