main.tex 3.28 KB
Newer Older
Leonard Guetta's avatar
OUF    
Leonard Guetta committed
1
\documentclass[12pt,a4paper]{report}
2

3
\usepackage[dvipsnames]{xcolor}
Leonard Guetta's avatar
Leonard Guetta committed
4
\usepackage[unicode,psdextra,final]{hyperref}
5
6
7
8
9
10
\hypersetup{
  colorlinks=true,
  linkcolor=Purple,
  citecolor=cyan,  
}
%\usepackage{classicthesis}
11
\usepackage{mystyle}
12
13
14
\usepackage{times}
\usepackage{sectsty}
\allsectionsfont{\scshape}
Leonard Guetta's avatar
Leonard Guetta committed
15
\iffalse
Leonard Guetta's avatar
Leonard Guetta committed
16
17
18
19
20
%%% Watermark
\usepackage{draftwatermark}
\SetWatermarkText{DRAFT}
\SetWatermarkScale{2}
%%%
Leonard Guetta's avatar
Leonard Guetta committed
21
\fi
Leonard Guetta's avatar
Leonard Guetta committed
22

Leonard Guetta's avatar
Leonard Guetta committed
23
%%% For line numbering (used for proodreading purposes)
Leonard Guetta's avatar
OUF    
Leonard Guetta committed
24
25
26

%% \usepackage[pagewise,displaymath, mathlines]{lineno}
%% \linenumbers
Leonard Guetta's avatar
Leonard Guetta committed
27

28
29
\begin{document}

30
\begin{titlepage}
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
   \includegraphics[width=0.4\textwidth]{logo_UP.jpg}
    
       \vspace*{1cm}
   \raggedleft
   {
   \scshape{\textbf{Université de Paris}} \par}
 \vspace{0.25cm}
 {\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}

      \vspace*{1.25cm}
      \centering
        {\Huge \scshape \textbf{Homology of strict $\omega$-categories}\par}

56
57
58
59
        % \vspace{0.5cm}
        % \LARGE
        % Thesis Subtitle
            
60
        \vspace{0.75cm}
61

62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
        {\Large
          
        \textbf{par Léonard Guetta}}





   \vfill 
   {\slshape Présentée et soutenue publiquement le 15 janvier 2021 \\
     devant un jury composé de : \par}
    \vspace{0.8cm}

 
    \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}
     
88
            
89
90
91
      \vspace{3cm}
      
      
92
     % \includegraphics[width=0.6\textwidth]{license.png}
Leonard Guetta's avatar
blabla    
Leonard Guetta committed
93
              %  \vspace*{-3cm}
94
  
95
\end{titlepage}
96

Leonard Guetta's avatar
Leonard Guetta committed
97
98
99
100
101
102
\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. }
Leonard Guetta's avatar
Leonard Guetta committed
103

Leonard Guetta's avatar
Leonard Guetta committed
104
105
\tableofcontents

Leonard Guetta's avatar
Leonard Guetta committed
106
\include{introduction}
107
\include{introduction_fr}
Leonard Guetta's avatar
Leonard Guetta committed
108
\include{omegacat}
Leonard Guetta's avatar
Leonard Guetta committed
109
\include{homtheo}
Leonard Guetta's avatar
Leonard Guetta committed
110
\include{hmtpy}
Leonard Guetta's avatar
Leonard Guetta committed
111
\include{hmlgy}
Leonard Guetta's avatar
Leonard Guetta committed
112
\include{contractible}
Leonard Guetta's avatar
Leonard Guetta committed
113
\include{2cat}
Leonard Guetta's avatar
Leonard Guetta committed
114
115

\addcontentsline{toc}{chapter}{Bibliography}
Leonard Guetta's avatar
Leonard Guetta committed
116
\bibliographystyle{alpha}
Leonard Guetta's avatar
Leonard Guetta committed
117
\bibliography{memoire}
118
\end{document}
Leonard Guetta's avatar
Leonard Guetta committed
119
120
121
122
123

%%% Local Variables:
%%% mode: latex
%%% TeX-master: t
%%% End: