Commit a120b417 authored by Leonard Guetta's avatar Leonard Guetta
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Did some bibliography fixxes

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\chapter{Homotopy and homology type of free $2$-categories}
\section{Preliminaries : the case of free $1$-categories}
\section{Preliminaries: the case of free $1$-categories}
In this section, we review some homotopical results concerning free ($1$-)categories that will be of great help in the sequel.
\begin{paragr}
A \emph{reflexive graph} $G$ consists of the data of two sets $G_0$ and $G_1$ together with
......@@ -313,7 +313,7 @@ We now apply Corollary \ref{cor:hmtpysquaregraph} and Proposition \ref{prop:hmtp
Note also that the hypothesis that $A\neq B$ was fundamental in the previous example as for $A=B$ the square is \emph{not} homotopy cocartesian.
\end{remark}
\section{Preliminaries : Bisimplicial sets}
\section{Preliminaries: bisimplicial sets}
\begin{paragr}
A \emph{bisimplicial set} is a presheaf over the category $\Delta \times \Delta$,
\[
......@@ -788,7 +788,7 @@ It also follows from Lemma \ref{lemma:binervthom} that the bisimplicial nerve in
This is an immediate consequence of Proposition \ref{prop:streetvsbisimplicial} and Corollary \ref{cor:bisimplicialsquare}.
\end{proof}
\section{Zoology of $2$-categories: Basic examples}
\section{Zoology of $2$-categories: basic examples}
\begin{paragr}\label{paragr:criterion2cat}
Before embarking on computations of homology and homotopy types of
$2$\nbd{}categories, let us recall the following particular case of Corollary
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......@@ -9,7 +9,7 @@
publisher={Narnia}
}
@article{ara2014vers,
title={Vers une structure de cat{\'e}gorie de mod{\`e}les {\`a} la {T}homason sur la cat{\'e}gorie des n-cat{\'e}gories strictes},
title={Vers une structure de cat{\'e}gorie de mod{\`e}les {\`a} la {T}homason sur la cat{\'e}gorie des n\nbd{}cat{\'e}gories strictes},
author={Ara, Dimitri and Maltsiniotis, Georges},
journal={Advances in Mathematics},
volume={259},
......@@ -22,10 +22,10 @@
author={Ara, Dimitri and Maltsiniotis, Georges},
journal={M{\'e}moires de la Soci{\'e}t{\'e} Math{\'e}matique de France},
year={2020},
note={To appear}
volume={165}
}
@article{ara2018theoreme,
title={Un th{\'e}or{\`e}me {A} de {Q}uillen pour les $\infty$-cat{\'e}gories strictes {I} : la preuve simpliciale},
title={Un th{\'e}or{\`e}me {A} de {Q}uillen pour les $\infty$\nbd{}cat{\'e}gories strictes {I} : la preuve simpliciale},
author={Ara, Dimitri and Maltsiniotis, Georges},
journal={Advances in Mathematics},
volume={328},
......@@ -34,13 +34,13 @@
publisher={Elsevier}
}
@article{ara2020comparaison,
title={Comparaison des nerfs $ n $-cat{\'e}goriques},
title={Comparaison des nerfs $n$\nbd{}cat{\'e}goriques},
author={Ara, Dimitri and Maltsiniotis, Georges},
journal={arXiv preprint arXiv:2010.00266},
year={2020}
}
@article{ara2020theoreme,
title={Un th{\'e}or{\`e}me {A} pour les $\infty$-cat{\'e}gories strictes {II} : la preuve $\infty$-cat{\'e}gorique},
title={Un th{\'e}or{\`e}me {A} de {Q}uillen pour les $\infty$-cat{\'e}gories strictes {II} : la preuve $\infty$-cat{\'e}gorique},
author={Ara, Dimitri and Maltsiniotis, Georges},
volume={4},
number={1},
......@@ -57,7 +57,7 @@ year={2020}
year={2020}
}
@article{ara2019quillen,
title={A Quillen Theorem B for strict $\infty$-categories},
title={A {Q}uillen Theorem {B} for strict $\infty$\nbd{}categories},
author={Ara, Dimitri},
journal={Journal of the London Mathematical Society},
volume={100},
......@@ -77,7 +77,7 @@ year={2020}
publisher={Academic Press}
}
@article{beke2001sheafifiableII,
title={Sheafifiable homotopy model categories, II},
title={Sheafifiable homotopy model categories, {II}},
author={Beke, Tibor},
journal={Journal of Pure and Applied Algebra},
volume={164},
......@@ -98,7 +98,7 @@ year={2020}
}
@book{bousfield1972homotopy,
title={Homotopy limits, completions and localizations},
author={Bousfield, Aldridge Knight and Kan, Daniel Marinus},
author={Bousfield, Aldridge K. and Kan, Daniel M.},
volume={304},
year={1972},
publisher={Springer Science \& Business Media}
......@@ -117,8 +117,8 @@ issn = "0001-8708",
publisher = "Elsevier"
}
@article{bullejos2003geometry,
title={On the geometry of 2-categories and their classifying spaces},
author={Bullejos, Manuel and Cegarra, Antonio M},
title={On the geometry of 2\nbd{}categories and their classifying spaces},
author={Bullejos, Manuel and Cegarra, Antonio M.},
journal={K-theory},
volume={29},
number={3},
......@@ -165,13 +165,13 @@ publisher = "Elsevier"
}
@phdthesis{crans1995combinatorial,
title={On Combinatorial Models for Higher Dimensional Homotopies},
author={Crans, Sjoerd Erik},
author={Crans, Sjoerd E.},
school={Universiteit Utrecht},
year={1995}
}
@article{duskin2002simplicial,
title={Simplicial matrices and the nerves of weak n-categories. I. Nerves of bicategories},
author={Duskin, John W},
title={Simplicial matrices and the nerves of weak n\nbd{}categories. {I}. Nerves of bicategories},
author={Duskin, John W.},
journal={Theory and Applications of Categories},
volume={9},
number={10},
......@@ -181,7 +181,7 @@ publisher = "Elsevier"
}
@article{dwyer1980simplicial,
title={Simplicial localizations of categories},
author={Dwyer, William G and Kan, Daniel M},
author={Dwyer, William G. and Kan, Daniel M.},
journal={J. Pure Appl. Algebra},
volume={17},
number={3},
......@@ -190,7 +190,7 @@ publisher = "Elsevier"
}
@incollection{dwyer1995homotopy,
title={Homotopy theories and model categories},
author={Dwyer, William G and Spalinski, Jan},
author={Dwyer, William G. and Spalinski, Jan},
booktitle={Handbook of Algebraic Topology},
pages={73--126},
publisher={ScienceDirect},
......@@ -198,7 +198,7 @@ publisher = "Elsevier"
}
@article{eilenberg1954groups,
title={On the groups {H}($\pi$,n), {II}: Methods of computation},
author={Eilenberg, Samuel and MacLane, Saunders},
author={Eilenberg, Samuel and Mac Lane, Saunders},
journal={Annals of Mathematics},
pages={49--139},
year={1954},
......@@ -206,7 +206,7 @@ publisher = "Elsevier"
}
@article{freyd1972categories,
title={Categories of continuous functors, {I}},
author={Freyd, Peter J and Kelly, G Max},
author={Freyd, Peter J. and Kelly, Max},
journal={Journal of pure and applied algebra},
volume={2},
number={3},
......@@ -252,10 +252,10 @@ publisher = "Elsevier"
publisher={Mathematical Sciences Publishers}
}
@unpublished{groth2013book,
title={Book project on Derivators, volume I},
title={Book project on {D}erivators, volume {I}},
author={Groth, Moritz},
year={2016},
note={Available at \url{http://webusers.imj-prg.fr/~georges.maltsiniotis/groth/Derivateurs}}
note={Available at \url{http://www.math.uni-bonn.de/~mrahn/monos/intro-to-der-1.pdf}}
}
@unpublished{grothendieckderivators,
title={Les D{\'e}rivateurs},
......@@ -264,7 +264,7 @@ year={~1990},
note={Available at \url{http://webusers.imj-prg.fr/~georges.maltsiniotis/groth/Derivateurs}}
}
@unpublished{grothendieck1991letter,
title={Lettre à Thomason},
title={Lettre à {T}homason},
author={Grothendieck, Alexandre},
year={1991},
note={Available at \url{http://webusers.imj-prg.fr/~georges.maltsiniotis/groth/Derivateurs}}
......@@ -314,13 +314,13 @@ year={2009}
}
@book{hirschhorn2009model,
title={Model categories and their localizations},
author={Hirschhorn, Philip S},
author={Hirschhorn, Philip S.},
year={2009},
publisher={American Mathematical Soc.}
}
@book{hopcroft1979introduction,
title={Introduction to automata theory, languages, and computation},
author={Hopcroft, John E and Ullman},
author={Hopcroft, John E. and Ullman, Jeffrey D.},
publisher={Addison-Wesley},
year={1979}
}
......@@ -408,7 +408,7 @@ publisher={Springer}
publisher={Citeseer}
}
@unpublished{maltsiniotis2001introduction,
title={Introduction à la théorie des dérivateurs, d'après Grothendieck},
title={Introduction à la théorie des dérivateurs, d'après {G}rothendieck},
author={Maltsiniotis, Georges},
year={2001},
note={Available at \url{http://webusers.imj-prg.fr/~georges.maltsiniotis/groth/Derivateurs}}
......@@ -459,13 +459,13 @@ note={In preparation}
}
@book{quillen1967homotopical,
title={Homotopical algebra},
author={Quillen, Daniel G},
author={Quillen, Daniel G.},
year={1967},
publisher={Springer}
}
@incollection{quillen1973higher,
title={Higher algebraic K-theory: I},
author={Quillen, Daniel},
author={Quillen, Daniel G.},
booktitle={Higher K-theories},
pages={85--147},
year={1973},
......@@ -533,7 +533,7 @@ note={In preparation}
}
@article{thomason1980cat,
title={Cat as a closed model category},
author={Thomason, Robert W},
author={Thomason, Robert W.},
journal={Cahiers de topologie et g{\'e}om{\'e}trie diff{\'e}rentielle cat{\'e}goriques},
volume={21},
number={3},
......@@ -542,7 +542,7 @@ note={In preparation}
}
@article{thomason1979homotopy,
title={Homotopy colimits in the category of small categories},
author={Thomason, Robert W},
author={Thomason, Robert W.},
booktitle={Mathematical Proceedings of the Cambridge Philosophical Society},
volume={85},
number={1},
......@@ -552,7 +552,7 @@ note={In preparation}
}
@book{weibel1995introduction,
title={An Introduction to Homological Algebra},
author={Weibel, Charles A},
author={Weibel, Charles A.},
volume={38},
year={1995},
publisher={Cambridge University Press}
......
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