[1] Ara, D., Higher quasi-categories vs higher Rezk spaces, J. K-Theory 14 (2014), no. 3, 701–749.CrossRefGoogle Scholar

[2] Ara, D., On the homotopy theory of Grothendieck ∞-groupoids, J. Pure Appl. Algebra 217 (2013), 1237–1278.CrossRefGoogle Scholar

[3] Ara, D., and Métayer, F., The Brown–Golasinski model structure on strict ∞-groupoids revisited, Homology, Homotopy Appl. 13 (2011), no. 1, 121–142.CrossRefGoogle Scholar

[4] Awodey, S., Category Theory, Oxford Logic Guides 49, Clarendon Press, 2006.Google Scholar

[5] Ayala, D., Francis, J., and Rozenblyum, N., Factorization homology I: higher categories (2015), available at arXiv:1504.04007.

[6] Ayala, D., Francis, J., and Rozenblyum, N., A stratified homotopy hypothesis (2015), available at arXiv:1502.01713.

[7] Badzioch, B., Algebraic theories in homotopy theory, Ann. of Math. (2) 155 (2002), no. 3, 895–913.CrossRefGoogle Scholar

[8] Baez, J.C., and Dolan, J., Higher-dimensional algebra. III, n-categories and the algebra of opetopes, Adv. Math. 135 (1998), no. 2, 145–206.Google Scholar

[9] Barwick, C., From operator categories to topological operads (2013), available at arXiv:1302.5756.

[10] Barwick, C., On left and right model categories and left and right Bousfield localizations, Homology, Homotopy Appl. 12 (2010), no. 2, 245–320.CrossRefGoogle Scholar

[11] Barwick, C., and Kan, D.M., Relative categories: another model for the homotopy theory of homotopy theories, Indag. Math. (N.S.) 23 (2012), no. 1–2, 42–68.CrossRefGoogle Scholar

[12] Barwick, C. and Kan, D.M., n-relative categories: a model for the homotopy theory of n-fold homotopy theories, Homology, Homotopy Appl. 15 (2013), no. 2, 281–300.

[13] Barwick, C., and Schommer-Pries, C., On the unicity of the homotopy theory of higher categories (2011), available at arXiv:1112.0040.

[14] Basic, M., and Nikolaus, T., Dendroidal sets as models for connective spectra, J. K-Theory 14 (2014), no. 3, 387–421.CrossRefGoogle Scholar

[15] Batanin, M.A., Monoidal globular categories as a natural environment for the theory of weak n-categories, Adv. Math. 136 (1998), 39–103.CrossRefGoogle Scholar

[16] Baues, H.-J., and Blanc, D., Comparing cohomology obstructions, J. Pure Appl. Algebra 215 (2011), 1420–1439.CrossRefGoogle Scholar

[17] Baues, H.-J., and Blanc, D., Higher order derived functors and the Adams spectral sequence, J. Pure Appl. Algebra 219 (2015), no. 2, 199–239.CrossRefGoogle Scholar

[18] Baues, H.-J., and Blanc, D., Stems and spectral sequences, Algebr. Geom. Topol. 10 (2010), 2061–2078.CrossRefGoogle Scholar

[19] Baues, H.-J., and Jibladze, M., Secondary derived functors and the Adams spectral sequence, Topology 45 (2006), 295–324.CrossRefGoogle Scholar

[20] Baues, H.-J., and Wirsching, G., Cohomology of small categories, J. Pure Appl. Algebra 38 (1985), 187–211.CrossRefGoogle Scholar

[21] Beke, T., Sheafifiable homotopy model categories, Math. Proc. Cambridge Philos. Soc. 129 (2000), 447–475.CrossRefGoogle Scholar

[22] Bénabou, J., Introduction to bicategories, Reports of the Midwest Category Seminar, Springer, 1967, pp. 1–77.CrossRefGoogle Scholar

[23] Berger, C., Iterated wreath product of the simplex category and iterated loop spaces, Adv. Math. 213 (2007), 230–270.CrossRefGoogle Scholar

[24] Bergner, J.E., A characterization of fibrant Segal categories, Proc. Amer. Math. Soc. 135 (2007), 4031–4037.CrossRefGoogle Scholar

[25] Bergner, J.E., Complete Segal spaces arising from simplicial categories, Trans. Amer. Math. Soc. 361 (2009), 525–546.Google Scholar

[26] Bergner, J.E., Equivalence of models for equivariant (∞, 1)-categories, Glasg. Math. J. 59 (2017), no. 1, 237–253.CrossRefGoogle Scholar

[27] Bergner, J.E., A model category structure on the category of simplicial categories, Trans. Amer. Math. Soc. 359 (2007), 2043–2058.CrossRefGoogle Scholar

[28] Bergner, J.E., Rigidification of algebras over multi-sorted theories, Algebr. Geom. Topol. 6 (2006), 1925–1955.CrossRefGoogle Scholar

[29] Bergner, J.E., Simplicial monoids and Segal categories, Contemp. Math. 431 (2007), 59–83.Google Scholar

[30] Bergner, J.E., Three models for the homotopy theory of homotopy theories, Topology 46 (2007), 397–436.CrossRefGoogle Scholar

[31] Bergner, J.E., Workshop on the homotopy theory of homotopy theories (2011), available at arXiv:1108.2001.

[32] Bergner, J.E., and Rezk, C., Comparison of models for (∞, n)-categories, I, Geom. Topol. 17 (2013), 2163–2202.Google Scholar

[33] Bergner, J.E., and Rezk, C., Comparison of models for (∞, n)-categories, II (2014), available at arXiv:1406.4182.

[34] Blanc, D., and Paoli, S., Segal-type algebraic models of n-types, Algebr. Geom. Topol. 14 (2014), no. 6, 3419–3491.Google Scholar

[35] Blanc, D., and Paoli, S., Two-track categories, J. K-Theory 8 (2011), no. 1, 59–106.CrossRefGoogle Scholar

[36] Boardman, J.M., and Vogt, R.M., Homotopy Invariant Algebraic Structures on Topological Spaces, Lecture Notes in Mathematics 347, Springer, 1973.CrossRefGoogle Scholar

[37] Bousfield, A.K., and Kan, D.M., Homotopy Limits, Completions, and Localizations, Lecture Notes in Mathematics 304, Springer, 1972.CrossRefGoogle Scholar

[38] Brown, R., Higgins, P.J., and Sivera, R., Nonabelian Algebraic Topology, with contributions by C.D., Wensley and S.V., Soloviev, EMS Tracts in Mathematics 15, European Mathematical Society, Zürich, 2011.Google Scholar

[39] Bullejos, M., Cegarra, A.M., and Duskin, J., On catn-groups and homotopy types, J. Pure Appl. Algebra 86 (1993), no. 2, 135–154.CrossRefGoogle Scholar

[40] Cabello, J.G., and Garzón, A.R., Closed model structures for algebraic models of n-types, J. Pure Appl. Algebra 103 (1995), no. 3, 287–302.CrossRefGoogle Scholar

[41] Cheng, E., Weak n-categories: comparing opetopic foundations, J. Pure Appl. Algebra 186 (2004), no. 3, 219–231.Google Scholar

[42] Cheng, E., Weak n-categories: opetopic and multitopic foundations, J. Pure Appl. Algebra 186 (2004), no. 2, 109–137.Google Scholar

[43] Chu, H., Haugseng, R., and Heuts, G., Two models for the homotopy theory of ∞-operads (2016), available at arXiv:1606.03826.

[44] Cisinski, D.-C., Batanin higher groupoids and homotopy types, Categories in Algebra, Geometry and Mathematical Physics, Contemporary Mathematics, 431, American Mathematical Society, 2007, pp. 171–186.Google Scholar

[45] Cisinski, D.-C., and Moerdijk, I., Dendroidal Segal spaces and ∞-operads, J. Topol. 6 (2013), no. 3, 675–704.Google Scholar

[46] Cisinski, D.-C., and Moerdijk, I., Dendroidal sets and simplicial operads, J. Topol. 6 (2013), no. 3, 705–756.Google Scholar

[47] Cisinski, D.-C., and Moerdijk, I., Dendroidal sets as models for homotopy operads, J. Topol. 4 (2011), no. 2, 257–299.CrossRefGoogle Scholar

[48] Cordier, J.M., and Porter, T., Vogt's theorem on categories of homotopy coherent diagrams, Math. Proc. Cambridge Philos. Soc. 100 (1986), 65–90.CrossRefGoogle Scholar

[49] Dugger, D., Combinatorial model categories have presentations, Adv. Math. 164 (2001), no. 1, 177–201.CrossRefGoogle Scholar

[50] Dugger, D., A Primer on Homotopy Colimits, available at pages.uoregon.edu/ ddugger/hocolim.pdf.

[51] Dugger, D., and Spivak, D.I., Mapping spaces in quasicategories, Algebr. Geom. Topol. 11 (2011), 263–325.CrossRefGoogle Scholar

[52] Dugger, D., and Spivak, D.I., Rigidification of quasicategories, Algebr. Geom. Topol. 11 (2011), 225–261.CrossRefGoogle Scholar

[53] Dwyer, W.G., and Kan, D.M., Calculating simplicial localizations, J. Pure Appl. Algebra 18 (1980), 17–35.CrossRefGoogle Scholar

[54] Dwyer, W.G., and Kan, D.M., A classification theorem for diagrams of simplicial sets, Topology 23 (1984), 139–155.CrossRefGoogle Scholar

[55] Dwyer, W.G., and Kan, D.M., Equivalences between homotopy theories of diagrams, Algebraic Topology and Algebraic K-Theory, Annals of Mathematics Studies 113, Princeton University Press, 1987, pp. 180–205.Google Scholar

[56] Dwyer, W.G., and Kan, D.M., Function complexes in homotopical algebra, Topology 19 (1980), 427–440.CrossRefGoogle Scholar

[57] Dwyer, W.G., and Kan, D.M., Simplicial localizations of categories, J. Pure Appl. Algebra 17 (1980), no. 3, 267–284.CrossRefGoogle Scholar

[58] Dwyer, W.G., Kan, D.M., and Smith, J.H., Homotopy commutative diagrams and their realizations, J. Pure Appl. Algebra 57 (1989), 5–24.CrossRefGoogle Scholar

[59] Dwyer, W.G., and Spalinski, J., Homotopy theories and model categories, Handbook of Algebraic Topology, Elsevier, 1995.Google Scholar

[60] Friedman, G., An elementary illustrated introduction to simplicial sets, Rocky Mountain J. Math. 42 (2012), no. 2, 353–423.CrossRefGoogle Scholar

[61] Gabriel, P., and Zisman, M., Calculus of Fractions and Homotopy Theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, 35, Springer, 1967.CrossRefGoogle Scholar

[62] Goerss, P.G., and Jardine, J.F., Simplicial Homotopy Theory, Progress in Mathematics, 174, Birkhäuser, 1999.CrossRefGoogle Scholar

[63] Gordon, R., Power, A.J., and Street, R., Coherence for tricategories, Mem. Amer. Math. Soc. 117 (1995), no. 558.Google Scholar

[64] Gurski, M.N., An algebraic theory of tricategories, Ph.D. Thesis, University of Chicago, 2006.Google Scholar

[65] Gurski, N., Nerves of bicategories as stratified simplicial sets, J. Pure Appl. Algebra 213 (2009), no. 6, 927–946.CrossRefGoogle Scholar

[66] Hatcher, A., Algebraic Topology, Cambridge University Press, 2002.Google Scholar

[67] Hermida, C., Makkai, M., and Power, J., On weak higher dimensional categories. I, J. Pure Appl. Algebra 154 (2000), no. 1–3, 221–246.CrossRefGoogle Scholar

[68] Heuts, G., Hinich, V., and Moerdijk, I., On the equivalence between Lurie's model and the dendroidal model for infinity-operads, Adv. Math. 302 (2016), 869–1043.CrossRefGoogle Scholar

[69] Hirschhorn, P. S., Model Categories and Their Localizations, Mathematical Surveys and Monographs 99, American Mathematical Society, 2003.Google Scholar

[70] Hirschowitz, A., and Simpson, C., Descente pour les n-champs (1998), available at arXiv:9807049.

[71] Hovey, M., Model Categories, Mathematical Surveys and Monographs 63, American Mathematical Society, 1999.Google Scholar

[72] Ilias, A., Model structure on the category of small topological categories, J. Homotopy Relat. Struct. 10 (2015), no. 1, 63–70.CrossRefGoogle Scholar

[73] Joyal, A., Quasi-categories and Kan complexes, J. Pure Appl. Algebra 175 (2002), 207–222.CrossRefGoogle Scholar

[74] Joyal, A., and Tierney, M., Quasi-categories vs Segal spaces, Contemp. Math. 431 (2007), 277–326.Google Scholar

[75] Kachour, C., Operadic definition of non-strict cells, Cah. Topol. Géom. Différ. Catég. 52 (2011), no. 4, 269–316.Google Scholar

[76] Kazhdan, D., and Varshavskiĭ, Ya., The Yoneda lemma for complete Segal spaces, Funktsional. Anal. i Prilozhen. 48 (2014), no. 2, 3–38; translation in Funct. Anal. Appl. 48 (2014), no. 2, 81–106.CrossRefGoogle Scholar

[77] Kock, J., Joyal, A., Batanin, M., and Mascari, J.-F., Polynomial functors and opetopes, Adv. Math. 224 (2010), 2690–2737.CrossRefGoogle Scholar

[78] Lack, S., A Quillen model structure for 2-categories, K-Theory 26 (2002), 171–205.CrossRefGoogle Scholar

[79] Lack, S., A Quillen model structure for bicategories, K-Theory 33 (2004), no. 3, 185–197.CrossRefGoogle Scholar

[80] Lack, S., A Quillen model structure for Gray-categories, J. K-Theory 8 (2011), 183–221.CrossRefGoogle Scholar

[81] Lafont, Y., Métayer, F., and Worytkiewicz, K., A folk model structure on omegacat, Adv. Math. 224 (2010), 1183–1231.CrossRefGoogle Scholar

[82] Lawvere, F.W., Functorial semantics of algebraic theories, Proc. Natl. Acad. Sci. USA 50 (1963), 869–872.CrossRefGoogle ScholarPubMed

[83] Leinster, T., Higher Operads, Higher Categories, London Mathematical Society Lecture Note Series 298, Cambridge University Press, 2004.CrossRefGoogle Scholar

[84] Leinster, T., Operads in higher-dimensional category theory, Theory Appl. Categ. 12 (2004), no. 3, 73–194.Google Scholar

[85] Leinster, T., A survey of definitions of n-category, Theory Appl. Categ. 10 (2002), 1–70.Google Scholar

[86]Loday, J.-L., Spaces with finitely many nontrivial homotopy groups, J. Pure Appl. Algebra 24 (1982), no. 2, 179–202.CrossRefGoogle Scholar

[87] Lurie, J., Higher Algebra, available at www.math.harvard.edu/∼1lurie/papers/ HA.pdf.

[88] Lurie, J., Higher Topos Theory, Annals of Mathematics Studies 170, Princeton University Press, 2009.Google Scholar

[89] Lurie, J., On the classification of topological field theories, Current Developments in Mathematics, 2008, International Press, 2009, pp. 129–280.

[90] Mac Lane, S., Categories for theWorking Mathematician, Second Edition, Graduate Texts in Mathematics 5, Springer, 1997.Google Scholar

[91] May, J.P., Simplicial Objects in Algebraic Topology, University of Chicago Press, 1967.Google Scholar

[92] Moerdijk, I., Lectures on dendroidal sets, Simplicial Methods for Operads and Algebraic Geometry, Advanced Courses in Mathematics – CRM, Barcelona, Birkhäuser, 2010, pp. 1–118.CrossRefGoogle Scholar

[93] Moerdijk, I., and Weiss, I., Dendroidal sets, Algebr. Geom. Topol. 7 (2007), 1441–1470.CrossRefGoogle Scholar

[94] Moerdijk, I., andWeiss, I., On inner Kan complexes in the category of dendroidal sets, Adv. Math. 221 (2009), no. 2, 343–389.CrossRefGoogle Scholar

[95] Morrison, S., andWalker, K., Higher categories, colimits, and the blob complex, Proc. Natl. Acad. Sci. USA 108 (2011), no. 20, 8139–8145.CrossRefGoogle ScholarPubMed

[96] Paoli, S., Weakly globular cat n-groups and Tamsamani's model, Adv. Math. 222 (2009), no. 2, 621–727.CrossRefGoogle Scholar

[97] Pellissier, R., Catégories enrichies faibles (2003), available at arXiv:0308246.

[98] Porter, T., n-types of simplicial groups and crossed n-cubes, Topology 32 (1993), no. 1, 5–24.CrossRefGoogle Scholar

[99] Quillen, D., Higher algebraic K-theory. I, Algebraic K-Theory, I: Higher KTheories (Proc. Conf., Battelle Memorial Inst., Seattle, Wash., 1972), Lecture Notes in Mathematics 341, Springer, 1973.Google Scholar

[100] Quillen, D., Homotopical Algebra, Lecture Notes in Mathematics 43, Springer, 1967.CrossRefGoogle Scholar

[101] Reedy, C.L., Homotopy Theory of Model Categories, available at www-math .mit.edu/˜psh.

[102] Rezk, C., A cartesian presentation of weak n-categories, Geom. Topol. 14 (2010), 521–571.Google Scholar

[103] Rezk, C., A model for the homotopy theory of homotopy theory, Trans. Amer. Math. Soc. 353 (2001), no. 3, 973–1007.CrossRefGoogle Scholar

[104] Riehl, E., Categorical Homotopy Theory, New Mathematical Monographs 24, Cambridge University Press, 2014.CrossRefGoogle Scholar

[105] Riehl, E., and Verity, D., The 2-category theory of quasi-categories, Adv. Math. 280 (2015), 549–642.CrossRefGoogle Scholar

[106] Riehl, E., and Verity, D., Fibrations and Yoneda's lemma in an ∞-cosmos, J. Pure Appl. Algebra 221 (2017), no. 3, 499–564.CrossRefGoogle Scholar

[107] Riehl, E., and Verity, D., Kan extensions and the calculus of modules for ∞-categories, Algebr. Geom. Topol. 17 (2017), no. 1, 189–271.CrossRefGoogle Scholar

[108] Robertson, M., The homotopy theory of simplicially enriched multicategories (2011), available at arXiv:1111.4146.

[109] Segal, G., Categories and cohomology theories, Topology 13 (1974), 293–312.CrossRefGoogle Scholar

[110] Simpson, C., Homotopy Theory of Higher Categories, NewMathematical Monographs 19, Cambridge University Press, 2012.Google Scholar

[111] Street, R., The algebra of oriented simplexes, J. Pure Appl. Algebra 49 (1987), no. 3, 283–335.CrossRefGoogle Scholar

[112] Strøm, A., The homotopy category is a homotopy category, Arch. Math. (Basel) 23 (1972), 435–441.CrossRefGoogle Scholar

[113] Tamsamani, Z., Sur les notions de n-categorie et n-groupóıde non-stricte via des ensembles multi-simpliciaux, K-Theory 16 (1999), no. 1, 51–99.CrossRefGoogle Scholar

[114] Thomason, R.W., Cat as a closed model category, Cah. Topol. Géom. Différ. Catég. 21 (1980), no. 3, 305–324.Google Scholar

[115] Töen, B., Homotopical and higher categorical structures in algebraic geometry (a view towards homotopical algebraic geometry) (2003), available at arXiv:0312262.

[116] Töen, B., Vers une axiomatisation de la théorie des catégories supérieures, K-Theory 34 (2005), no. 3, 233–263.CrossRefGoogle Scholar

[117] Verity, D.R.B., Weak complicial sets I: basic homotopy theory, Adv. Math. 219 (2008), no. 4, 1081–1149.CrossRefGoogle Scholar

[118] Weibel, C.A., An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics 38, Cambridge University Press, 1994.CrossRefGoogle Scholar