Commit a120b417 by Leonard Guetta

### Did some bibliography fixxes

parent cb36cb3c
 \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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