Commit 03753ab9 authored by Leonard Guetta's avatar Leonard Guetta
Browse files

Chapitre 2 à reprendre

parent 48fd8f1e
\chapter{Homotopical algebra}
The present chapter sticks out from the others as it contains no original results. Its goal is simply to introduce the langage and tools of homotopical algebra that we shall need in the rest of the dissertation. In consequence, most of the results are simply asserted and the reader will find references to litterature for the proofs. The main notion of homotopical algebra we are aiming for is the one of \emph{homotopy colimits} and the language we chose to express this notion is the one given by the theory of Grothendieck's \emph{derivators} \cite{grothendieckderivators}. Let us quickly motive this choice for the reader unfamiliar with this theory.
\section{Localization, derivation}
\begin{paragr}\label{paragr:loc}
......
......@@ -2,11 +2,13 @@
\usepackage{mystyle}
\iffalse
%%% Watermark
\usepackage{draftwatermark}
\SetWatermarkText{DRAFT}
\SetWatermarkScale{2}
%%%
\fi
\title{Homology of strict $\omega$-categories}
\author{Léonard Guetta}
......@@ -15,7 +17,9 @@
\maketitle
\tableofcontents
\abstract{In this dissertation, we study the homology of strict $\oo$-categories. More precisely, we intend to compare the ``classical'' homology of an $\oo$-category (defined as the homology of its Street nerve) with its polygraphic homology. Along the way, we prove several important result concerning free strict $\oo$\nbd-categories over polygraphs-or-computad and concerning the homotopy theory of strict $\oo$\nbd-categories. }
\include{omegacat}
\include{homtheo}
\include{hmtpy}
......
......@@ -175,6 +175,12 @@ year={2020}
journal={arXiv preprint arXiv:1202.3359},
year={2012}
}
@unpublished{grothendieckderivators,
title={Les D{\'e}rivateurs},
author={Grothendieck, Alexandre},
year={~1990},
note={Available at \url{http://webusers.imj-prg.fr/~georges.maltsiniotis/groth/Derivateurs}}
}
@article{guetta2020polygraphs,
title={Polygraphs and discrete Conduch{\'e} $\omega$-functors},
author={Guetta, L{\'e}onard},
......@@ -245,7 +251,7 @@ year={2020}
@article{makkai2005word,
title={The word problem for computads},
author={Makkai, Michael},
journal={Available on the author’s web page http://www. math. mcgill. ca/makkai},
journal={Available on the author’s web page \url{http://www. math. mcgill. ca/makkai}},
year={2005},
publisher={Citeseer}
}
......
......@@ -9,6 +9,10 @@
\usepackage{chngpage} %allows for temporary adjustment of margin
% url, references
\usepackage{url}
% Maths packages
\usepackage{amsmath,amssymb,amsthm}
......
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