[1] J. Adámek and J. Rosický. Locally Presentable and Accessible Categories,
volume 189 of London Mathematical Society Lecture Note Series. Cambridge University Press, 1994.
[2] J. C. Baez and J. Dolan. Higher-dimensional algebra and topological quantum field theory. Journal of Mathematical Physics, 36(11):6073–6105, 1995.
http://arxiv.org/abs/q-alg/9503002.
[3] M. Batanin and M. Markl. Crossed interval groups and operations on the
hochschild cohomology. Journal of Noncommutative Geometry, pages 655–
693, 2014.
[4] J. Bénabou. Introduction to bicategories, pages 1–77. Lecture Notes in
Mathematics 47. Springer-Verlag, 1967.
[5] C. Berger and I. Moerdijk. Axiomatic homotopy theory for operads. Commentarii Mathematici Helvetici, 78(4):805–831, 2003.
[6] J. M. Boardman and R. M. Vogt. Homotopy Invariant Algebraic Structures on Topological Spaces. Number 347 in Lecture Notes in Mathematics.
Springer-Verlag, 1973.
[7] M. Bökstedt, W. C. Hsiang, and I. Madsen. The cyclotomic trace and
algebraic K-theory of spaces. Inventiones Mathematicae, 111(3):465–539,
1993.
[8] F. Borceux. Handbook of Categorical Algebra 1. Number 50 in Encyclopedia
of Mathematics and its Applications. Cambridge University Press, 1994.
[9] F. Borceux. Handbook of Categorical Algebra 2. Number 51 in Encyclopedia
of Mathematics and its Applications. Cambridge University Press, 1994.
[10] M. Buckley. Fibred 2-categories and bicategories. Journal of Pure and
Applied Algebra, 218:1034–1074, 06 2014.
[11] R. W. Carroll. Calculus revisited, volume 554 of Mathematics and its Applications. Kluwer Academic Publishers, Dordrecht, 2002.
[12] A. Connes. Cohomologie cyclique et foncteurs Extn . Comptes Rendus des
Séances de l’Académie des Sciences. Série I. Mathématique, 296(23):953–
958, June 1983.
167
[13] A. Connes. Noncommutative differential geometry. Publications Mathématiques des l’IHÉS, 62:257–360, 1985.
[14] A. Connes. Noncommutative geometry. Academic Press, Inc., San Diego,
CA, 1994.
[15] A. S. Corner and N. Gurski. Operads with general groups of equivariance,
and some 2-categorical aspects of operads in cat. arXiv:1312.5910, 2013.
[16] A. Dold. Homology of symmetric products and other functors of complexes.
Annals of Mathematics, 68(1):54–80, 1958.
[17] A. Dold and D. Puppe. Homologie nicht-additiver Funktoren. Anwendungen. Annales de l’Institut Fourier, 11:201–312, 1961.
[18] V. G. Drinfel0 d. Quantum groups. In Proceedings of the International
Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif., 1986), pages 798–
820. American Mathematical Society, 1987.
[19] E. J. Dubuc. Adjoint triangles, volume 61 of Lecture Notes in Mathematics,
pages 69–91. Springer-Verlag, Berlin, Heidelberg, 1968.
[20] W. G. Dwyer and D. M. Kan. Normalizing the cyclic modules of connes.
Commentarii Mathematici Helvetici, 60(1):582–600, December 1985.
[21] T. Dyckerhoff and M. Kapranov. Crossed simplicial groups and structured
surfaces. arXiv:1403.5799, 2014.
[22] R. Dyckhoff and W. Tholen. Exponentiable morphisms, partial products and pullback complements. Journal of Pure and Applied Algebra,
49(1):103–116, 1987.
[23] A. D. Elmendorf. A simple formula for cyclic duality. Proceedings of the
American Mathematical Society, 118(3):709–711, 1993.
[24] Z. Fiedorowicz and J-L Loday. Crossed simplicial groups and their associated homology. Transactions of the American Mathematical Society,
326(1):57–87, 1991.
[25] P.J. Freyd and G.M. Kelly. Categories of continuous functors, I. Journal of
Pure and Applied Algebra, 2(3):169–191, 1972. Erratum ibid. 4(2014):121.
[26] I. Gelfand and M. Naimark. On the imbedding of normed rings into the
ring of operators in Hilbert space. In C ∗ -algebras: 1943–1993 (San Antonio, TX, 1993), volume 167 of Contemporary Mathematics, pages 2–19.
American Mathematical Society, 1994. Corrected reprint of the 1943 original.
[27] D. Gepner and R. Haugseng. Enriched ∞-categories via non-symmetric
∞-operads. Advances in Mathematics, 279:575–716, 2015.
[28] E. Getzler and J. D. S. Jones. The cyclic homology of crossed product
algebras. Journal für die Reine und Angewandte Mathematik. [Crelle’s
Journal], 445:161–174, 1993.
168
[29] E. Goursat. Sur les substitutions orthogonales et les divisions régulières
de l’espace. Annales scientifiques de l’École Normale Supérieure, 6:9–102,
1889.
[30] A. Grothendieck. Revêtements étales et groupe fondamental (SGA 1), volume 224 of Lecture Notes in Mathematics. Springer-Verlag, 1971. Séminaire
de Géométrie Algébrique I.
[31] N. Gurski. Operads, tensor products, and the categorical borel construction. arXiv:1508.04050, 2015.
[32] C. Hermida. Some properties of fib as a fibred 2-category. Journal of Pure
and Applied Algebra, 134(1):83–109, 1999.
[33] C. Hermida. Representable multicategories. Advances in Mathematics,
151(2):164–225, 2000.
[34] P. Hirschhorn. Model Categories and Their Localizations. Number 99 in
Mathematical Surveys and Monographs. American Mathematical Society,
2009.
[35] G. Hochschild, B. Kostant, and A. Rosenberg. Differential forms on regular affine algebras. Transactions of the American Mathematical Society,
102:383–408, 1962.
[36] M. Hovey. Model Categories. Number 63 in Mathematical surveys and
monographs. Amer Mathematical Society, 2007.
[37] P. T. Johnstone. Topos Theory. LMS Monograph 10. Academic Press,
London, 1977.
[38] J. D. S. Jones. Cyclic homology and equivariant homology. Inventiones
Mathematicae, 87(2):403–423, 1987.
[39] A. Joyal.
Disks, duality and θ-categories.
https://ncatlab.org/nlab/files/JoyalThetaCategories.pdf.
available
at
[40] A. Joyal. Quasi-categories and kan complexes. Journal of Pure and Applied
Algebra, 175(1âĂŞ3):207–222, 2002. Special Volume celebrating the 70th
birthday of Professor Max Kelly.
[41] A. Joyal. The theory of quasi-categories and its applications. lectures at
CRM Barcelona February 2008, 2008.
[42] A. Joyal and R. Street. Pullbacks equivalent to pseudopullbacks. Cahiers
de Topologie et Géométrie Différentielle Catégoriques, 34(2):153–156, 1993.
[43] A. Joyal and M. Tierney. Strong stacks and classifying spaces. In A. Carboni, M. C. Pedicchio, and G. Rosolini, editors, Category Theory, pages
213–236, Berlin, Heidelberg, 1991. Springer Berlin Heidelberg. Proceedings of the International Conference held in Como, Italy, July 22–28, 1990.
[44] D. M. Kan. Functors involving c.s.s. complexes. Transactions of the American Mathematical Society, 87:330–346, 1958.
169
[45] G. M. Kelly. Basic concepts of enriched category theory. Reprints in Theory
and Applications of Categories, 10:1–136, 2005. Reprint of the 1982 original
[Cambridge Univ. Press, Cambridge; MR0651714].
[46] G. M. Kelly and F. W. Lawvere. On the complete lattice of essential
localizations. Bulletin de la Société Mathématique de Belgique, Série A,
41(2):289–319, 1989.
[47] R. Krasauskas. Skew-simplicial groups. Lithuanian Mathematical Journal,
27(1):47–54, 1987. Translated from Litovski˘ı Matematichenski˘ı Sbornik
(Lietuvos Matematikos Rinkinys), 27(1):89–99.
[48] S. Lack. A quillen model structure for bicategories. K-Theory, 33:185–197,
11 2004.
[49] S. Lack. A 2-categories companion. In John C. Baez and J. Peter May,
editors, Towards higher categories, IMA volumes in mathematics and its
applications, pages 105–191. Springer, 2010.
[50] T. Leinster. Basic bicategories. arXiv:math/9810017, 1998.
[51] T. Leinster. Higher operads, higher categories. Number 298 in London
Mathematical Society Lecture Note Series. Cambridge University Press,
Cambridge, 2004.
[52] J-L. Loday. Free loop space and homology. In Janko Latschev and
Alexandru Oancea, editors, Free loop spaces in geometry and topology, volume 24 of IRMA Lectures in Mathematics and Theoretical Physics, pages
137–156. European Mathematical Society Publishing House, Zürich, 2015.
arXiv:1110.0405.
[53] J. Lurie. Higher Topos Theory. Number 170 in Annals of Mathematics
Studies. Princeton University Press, 2009.
[54] J. Lurie. Higher algebra. see author’s webpage, September 2014.
[55] S. MacLane. Categories for the Working Mathematician. Number 5 in
Graduate Texts in Mathematics. Springer-Verlag, second ed. edition, 1998.
[56] M. Makkai and A. M. Pitts. Some results on locally finitely presentable categories. Transactions of the American Mathematical Society, 299(2):473–
496, 1987.
[57] J. P. May. The geometry of iterated loop spaces, volume 271 of Lectures
Notes in Mathematics. Springer-Verlag, Berlin-New York, 1972.
[58] J. P. May and R. Thomason. The uniqueness of infinite loop space machines. Topology, 17(3):205–224, 1978.
[59] J-P. Meyer. Bar and cobar constructions, I. Journal of Pure and Applied
Algebra, 33(2):163–207, 1984.
[60] J-P. Meyer. Bar and cobar constructions, II. Journal of Pure and Applied
Algebra, 43(2):179–210, 1986.
170
[61] S. Montgomery. Hopf algebras and their actions on rings, volume 82 of
CBMS Regional Conference Series in Mathematics. American Mathematical Society, 1993.
[62] T. Nikolaus and P. Scholze.
arXiv:1707.01799, 2017.
On topological cyclic homology.
[63] V. Nistor. Group cohomology and the cyclic cohomology of crossed products. Inventiones mathematicae, 99(1):411–424, December 1990.
[64] H-E. Porst. On categories of monoids, comonoids, and bimonoids. Quaestiones Mathematicae, 31(2):127–139, 2008.
[65] D. Quillen. Homotopical algebra. Number 43 in Lecture Notes in Mathematics. Springer-Verlag, 1967.
[66] D. Quillen. Higher algebraic K-theory: I. In H. Bass, editor, Higher KTheories: Proceedings of the Conference held at the Seattle Research Center
of the Battelle Memorial Institute, from August 28 to September 8, 1972,
pages 85–147, Berlin, Heidelberg, 1973. Springer-Verlag.
[67] C. Rezk. A model category for categories. preprint, available at author’s
webpage, September 2000.
[68] G. Segal. Classifying spaces and spectral sequences. Publications Mathématiques de I’HÉS, 34:105–112, 1968.
[69] J-P. Serre. Faisceaux algébriques cohérents. Annals of Mathematics. Second
Series, 61:197–278, 1955.
[70] C. Simpson. Homotopy theory of higher categories, volume 19 of New Mathematical Monographs. Cambridge University Press, Cambridge, 2012.
[71] James Dillon Stasheff. Homotopy associativity of H-spaces. I, II. Transactions of the American Mathematical Society, 108:293–312, 1963.
[72] R. Street and D. Verity. The comprehensive factorization and torsors.
Theory and Applications of Categories, 23(3):42–76, 2010.
[73] R. G. Swan. Vector bundles and projective modules. Transactions of the
American Mathematical Society, 105:264–277, 1962.
[74] R. W. Thomason. Cat as a closed model category. Cahiers Topologie Géom.
Différentielle Catégoriques, 21(3):305–324, 1980.
[75] N. Wahl. Ribbon braids and related operads. PhD thesis, University of
Oxford, 2001.
[76] W. Zhang. Group operads and homotopy theory. arXiv:1111.7090, part of
the Ph.D. thesis, 2011.
171
...
論文の公開元へ
