D. Anick, On the homology of associative algebras. Transactions of the, pp.641-659, 1986.

M. Batanin, Monoidal Globular Categories As a Natural Environment for the Theory of Weakn-Categories, Advances in Mathematics, vol.136, issue.1, pp.39-103, 1998.
DOI : 10.1006/aima.1998.1724

T. Beke, Sheafifiable homotopy model categories, Mathematical Proceedings of the Cambridge Philosophical Society, vol.129, issue.3, pp.447-475, 2000.
DOI : 10.1017/S0305004100004722

T. Beke, Sheafifiable homotopy model categories, II, Journal of Pure and Applied Algebra, vol.164, issue.3, pp.307-324, 2001.
DOI : 10.1016/S0022-4049(01)00075-5

A. Burroni, Higher-dimensional word problem In Category theory and computer science, number 530 in Lecture Notes in Computer Science, pp.94-105, 1991.

A. Burroni, Higher-dimensional word problems with applications to equational logic, Theoretical Computer Science, vol.115, issue.1, pp.43-62, 1993.
DOI : 10.1016/0304-3975(93)90054-W

P. Gabriel and M. Zisman, Calculus of Fractions and Homotopy Theory, 1967.
DOI : 10.1007/978-3-642-85844-4

R. Garner, Understanding the small object argument Applied Categorical Structures, 2008.

Y. Guiraud, The three dimensions of proofs, Annals of Pure and Applied Logic, vol.141, issue.1-2, pp.266-295, 2006.
DOI : 10.1016/j.apal.2005.12.012
URL : https://hal.archives-ouvertes.fr/hal-00092212

Y. Guiraud, Two polygraphic presentations of Petri nets, Theoretical Computer Science, vol.360, issue.1-3, pp.124-146, 2006.
DOI : 10.1016/j.tcs.2006.02.015
URL : https://hal.archives-ouvertes.fr/hal-00092209

M. Hovey, Model Categories, 1999.

A. Joyal and M. Tierney, Strong stacks and classifying spaces, Category Theory Proc. Int. Conf., Como/Italy 1990, number 1488 in Lect. Notes Math, pp.213-236, 1991.
DOI : 10.2307/1970725

Y. Kobayashi, Complete rewriting systems and homology of monoid algebras, Journal of Pure and Applied Algebra, vol.65, issue.3, pp.263-275, 1990.
DOI : 10.1016/0022-4049(90)90106-R

S. Lack, A Quillen model structure for 2-categories. K-Theory, pp.171-205, 2002.

S. Lack, A Quillen model structure for bicategories. K-Theory, pp.185-197, 2004.

Y. Lafont, Algebra and geometry of rewriting Applied Categorical Structures, pp.415-437, 2007.

Y. Lafont and F. Métayer, Polygraphic resolutions and homology of monoids, Journal of Pure and Applied Algebra, vol.213, issue.6, pp.947-968, 2009.
DOI : 10.1016/j.jpaa.2008.10.005
URL : https://hal.archives-ouvertes.fr/hal-00148370

F. Métayer, Resolutions by polygraphs Theory and Applications of Categories, pp.148-184, 2003.

F. Métayer, Cofibrant objects among higher-dimensional categories. Homology, Homotopy and Applications, pp.181-203, 2008.

J. Power, An n-categorical pasting theorem, Category Theory, Proc. Int. Conf., Como/Italy 1990, number 1488 in Lect. Notes Math, pp.326-358, 1991.

D. Quillen, Homotopical Algebra, Lecture Notes in Mathematics, vol.43, 1967.
DOI : 10.1007/BFb0097438

J. Rosicky and W. Tholen, Left-determined model categories and universal homotopy theories, Transactions of the American Mathematical Society, vol.355, issue.09, pp.3611-3623, 2003.
DOI : 10.1090/S0002-9947-03-03322-1

C. Squier, Word problems and a homological finiteness condition for monoids, Journal of Pure and Applied Algebra, vol.49, issue.1-2, pp.201-217, 1987.
DOI : 10.1016/0022-4049(87)90129-0

C. Squier, F. Otto, and Y. Kobayashi, A finiteness condition for rewriting systems, Theoretical Computer Science, vol.131, issue.2, pp.271-294, 1994.
DOI : 10.1016/0304-3975(94)90175-9

R. Street, Limits indexed by category-valued 2-functors, Journal of Pure and Applied Algebra, vol.8, issue.2, pp.149-181, 1976.
DOI : 10.1016/0022-4049(76)90013-X
URL : http://doi.org/10.1016/0022-4049(76)90013-x

K. Worytkiewicz, K. Hess, P. Parent, and A. Tonks, A model structure ?? la Thomason on <mml:math altimg="si1.gif" display="inline" overflow="scroll" xmlns:xocs="http://www.elsevier.com/xml/xocs/dtd" xmlns:xs="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns="http://www.elsevier.com/xml/ja/dtd" xmlns:ja="http://www.elsevier.com/xml/ja/dtd" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:tb="http://www.elsevier.com/xml/common/table/dtd" xmlns:sb="http://www.elsevier.com/xml/common/struct-bib/dtd" xmlns:ce="http://www.elsevier.com/xml/common/dtd" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:cals="http://www.elsevier.com/xml/common/cals/dtd"><mml:mstyle mathvariant="bold"><mml:mi>2</mml:mi></mml:mstyle><mml:mtext><ce:bold>-</ce:bold></mml:mtext><mml:mstyle mathvariant="bold"><mml:mi>Cat</mml:mi></mml:mstyle></mml:math>, Journal of Pure and Applied Algebra, vol.208, issue.1, pp.205-236, 2007.
DOI : 10.1016/j.jpaa.2005.12.010