The formal theory of Tannaka duality
Astérisque, no. 357 (2013) , 148 p.
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@book{AST_2013__357__R1_0,
     author = {Sch\"appi, Daniel},
     title = {The formal theory of Tannaka duality},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {357},
     year = {2013},
     zbl = {1314.18008},
     mrnumber = {3185459},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2013__357__R1_0/}
}
Schäppi, Daniel. The formal theory of Tannaka duality. Astérisque, no. 357 (2013), 148 p. http://numdam.org/item/AST_2013__357__R1_0/

[1] H. Appelgate & M. Tierney - "Categories with models", in Sem. on Triples and Categorical Homology Theory (ETH, Zürich, 1966/67), Springer, 1969, p. 156-244. | Article | MR 242916 | Zbl 0188.28204

[2] J. Baez & J. Dolan - "Higher-dimensional algebra III: n-categories and the algebra of opetopes", preprint arXiv:9702014. | MR 1620826 | Zbl 0909.18006

[3] J. Bénabou - "Les distributeurs", in Rapport No. 33, Séminaire de Math. Pures, Univ. Catholique de Louvain, 1973.

[4] F. Borceux - Handbook of categorical algebra.1, Encyclopedia of Mathematics and its Applications, vol. 50, Cambridge Univ. Press, 1994. | MR 1291599 | Zbl 0803.18001

[5] A. Bruguières - "On a Tannakian theorem due to Nori", unpublished, available on http://www.math.univ-montp2.fr/~bruguieres/ (July 10, 2011), 2004.

[6] A. Bruguières, S. Lack & A. Virelizier - "Hopf monads on monoidal categories", preprint arXiv:1003.1920, 2010. | MR 2793022 | Zbl 1233.18002

[7] A. Bruguières & A. Virelizier - "Hopf monads", Adv. Math. 215 (2007), p. 679-733. | Article | MR 2355605 | Zbl 1168.18002

[8] D. Chikhladze, S. Lack & R. Street -"Hopf monoidal comonads", preprint arXiv: 1002.1122, 2010. | MR 2770074 | Zbl 1250.18006

[9] G. S. H. Cruttwell - "Normed spaces and the change of base for enriched categories", Ph.D. Thesis, Dalhousie University, 2008, available on http://geoff.reluctantm.com/publications/GThesis.pdf (October 21, 2011). | MR 2713532

[10] B. J. Day - "Linear monads", Bull. Austral. Math. Soc. 17 (1977), p. 177-192. | Article | MR 466260 | Zbl 0359.18007

[11] B. J. Day, "Enriched Tannaka reconstruction", J. Pure Appl. Algebra 108 (1996), p. 17-22. | Article | MR 1382240 | Zbl 0857.18011

[12] B. J. Day, P. Mccrudden & R. Street - "Dualizations and antipodes", Appl. Categ. Structures 11 (2003), p. 229-260. | Article | MR 1990034 | Zbl 1023.18008

[13] B. J. Day & C. Pastro - "Note on Frobenius monoidal functors", New York J. Math. 14 (2008), p. 733-742. | EuDML 117424 | MR 2465800 | Zbl 1178.18006

[14] B. J. Day & R. Street - "Monoidal bicategories and Hopf algebroids", Adv. Math. 129 (1997), p. 99-157. | Article | MR 1458415 | Zbl 0910.18004

[15] P. Deligne - "Catégories tannakiennes", in The Grothendieck Festschrift, Vol. II, Progr. Math., vol. 87, Birkhäuser, 1990, p. 111-195. | MR 1106898 | Zbl 0727.14010

[16] P. Deligne & J. S. Milne - "Tannakian categories", in Hodge cycles, motives, and Shimura varieties, Lecture Notes in Math., vol. 900, Springer, 1982, p. 101- 228. | Article | MR 654325 | Zbl 0477.14004

[17] E. J. Dubuc - "Adjoint triangles", in Reports of the Midwest Category Seminar, II, Springer, 1968, p. 69-91. | Article | MR 233864 | Zbl 0172.02103

[18] E. J. Dubuc, Kan extensions in enriched category theory, Lecture Notes in Math., vol. 145, Springer, 1970. | MR 280560 | Zbl 0228.18002

[19] S. Eilenberg & G. M. Kelly - "Closed categories", in Proc. Conf. Categorical Algebra (La Jolla, Calif, 1965), Springer, 1966, p. 421-562. | Article | MR 225841 | Zbl 0192.10604

[20] J.-M. Fontaine & G. Laffaille - "Construction de représentations p-adiques", Ann. Sci. École Norm. Sup. 15 (1982), p. 547-608. | Article | EuDML 82106 | Numdam | MR 707328 | Zbl 0579.14037

[21] R. Gordon & A. J. Power - "Enrichment through variation", J. Pure Appl. Algebra 120 (1997), p. 167-185. | Article | MR 1466618 | Zbl 0881.18006

[22] R. Gordon, A. J. Power & R. Street - "Coherence for tricategories", Mem. Amer. Math. Soc. 117 (1995). | MR 1261589 | Zbl 0836.18001

[23] N. Gurski - "An algebraic theory of tricategories", Ph.D. Thesis, University of Chicago, 2006, available on http://www.math.yale.edu/~mg622/tricats.pdf (October 12, 2011).

[24] P. H. Hai - "Tannaka-Krein duality for Hopf algebroids", Israel J. Math. 167 (2008), p. 193-225. | Article | MR 2448024 | Zbl 1169.18003

[25] M. Hovey - "Homotopy theory of comodules over a Hopf algebroid", in Homotopy theory: relations with algebraic geometry, group cohomology, and algebraic K-theory, Contemp. Math., vol. 346, Amer. Math. Soc., 2004, p. 261-304. | MR 2066503 | Zbl 1067.18012

[26] S. R. Johnsen - "Small Cauchy completions", J. Pure Appl. Algebra 62 (1989), p. 35-45. | Article | MR 1026873 | Zbl 0696.18004

[27] A. Joyal & R. Street - "The geometry of tensor calculus. I", Adv. Math. 88 (1991), p. 55-112. | Article | MR 1113284 | Zbl 0738.18005

[28] A. Joyal & R. Street, "Braided tensor categories", Adv. Math. 102 (1993), p. 20-78. | Article | MR 1250465 | Zbl 0817.18007

[29] G. M. Kelly - "Doctrinal adjunction", in Category Seminar (Proc. Sem., Sydney, 1972/1973), Springer, 1974, p. 257-280. Lecture Notes in Math., Vol. 420. | Article | MR 360749 | Zbl 0334.18004

[30] G. M. Kelly, "Structures defined by finite limits in the enriched context. I", Cahiers Topologie Géom. Différentielle 23 (1982), p. 3-42. | EuDML 91287 | Numdam | MR 648793 | Zbl 0538.18006

[31] G. M. Kelly, "Basic concepts of enriched category theory", Repr. Theory Appl. Categ. 10 (2005). | MR 2177301 | Zbl 1086.18001

[32] G. M. Kelly, "On the operads of J. P. May", Repr. Theory Appl. Categ. 13 (2005), p. 1-13. | MR 2177746 | Zbl 1082.18009

[33] G. M. Kelly & R. Street - "Review of the elements of 2-categories", in Category Seminar (Proc. Sem., Sydney, 1972/1973), Springer, 1974, p. 75-103. Lecture Notes in Math., Vol. 420. | Article | MR 357542 | Zbl 0334.18016

[34] S. Lack - "A coherent approach to pseudomonads", Adv. Math. 152 (2000), p. 179-202. | Article | MR 1764104 | Zbl 0971.18008

[35] S. Lack, "A Quillen model structure for 2-categories", K-Theory 26 (2002), p. 171-205. | Article | MR 1931220 | Zbl 1017.18005

[36] S. Lack, "A 2-categories companion", in Towards higher categories, IMA Vol. Math. Appl., vol. 152, Springer, 2010, p. 105-191. | Article | MR 2664622 | Zbl 1223.18003

[37] S. Lack, "A Quillen model structure for Gray-categories", preprint arXiv:1001.2366, 2010. | MR 2842929 | Zbl 1257.18013

[38] F. W. Lawvere - "Metric spaces, generalized logic, and closed categories", Rend. Sem. Mat. Fis. Milano 43 (1973), p. 135-166. | Article | MR 352214 | Zbl 0335.18006

[39] I. López Franco - "Autonomous pseudomonoids", Ph.D. Thesis, University of Cambridge, 2009, available on http://www.dspace.cam.ac.uk/handle/1810/ 219201 (October 28, 2011).

[40] I. López Franco, R. Street & R. Wood - "Duals invert", Applied Categorical Structures 19 (2011), p. 321-361. | Article | MR 2772612 | Zbl 1259.18002

[41] S. Majid - "Tannaka-Kreĭn theorem for quasi-Hopf algebras and other results", in Deformation theory and quantum groups with applications to mathematical physics (Amherst, MA, 1990), Contemp. Math., vol. 134, Amer. Math. Soc., 1992, p. 219-232. | Article | MR 1187289 | Zbl 0788.17012

[42] P. Mccrudden - "Balanced coalgebroids", Theory Appl. Categ. 7 (2000), p. No. 6, 71-147. | EuDML 120925 | MR 1764504 | Zbl 0960.18005

[43] P. Mccrudden, "Categories of representations of coalgebroids", Adv. Math. 154 (2000), p. 299-332. | Article | MR 1784678 | Zbl 0968.18004

[44] P. Mccrudden, "Tannaka duality for Maschkean categories", J. Pure Appl. Algebra 168 (2002), p. 265-307. | Article | MR 1887160 | Zbl 0999.18007

[45] B. Pareigis - "A noncommutative noncocommutative Hopf algebra in "nature"", J. Algebra 70 (1981), p. 356-374. | Article | MR 623814 | Zbl 0463.18003

[46] B. Pareigis, "Reconstruction of hidden symmetries", J. Algebra 183 (1996), p. 90-154. | Article | MR 1397390 | Zbl 0859.16034

[47] R. Penrose - "Applications of negative dimensional tensors", in Combinatorial Mathematics and its Applications (Proc. Conf, Oxford, 1969), Academic Press, 1971, p. 221-244. | MR 281657 | Zbl 0216.43502

[48] N. Saavedra Rivano - Catégories Tannakiennes, Lecture Notes in Math., vol. 265, Springer, 1972. | MR 338002 | Zbl 0241.14008

[49] J-P. Serre - Corps locaux, Hermann, 1968. | MR 354618

[50] M. Shulman - "Constructing symmetric monoidal bicategories", preprint arXiv:1004.0993, 2010.

[51] R. Street - "The formal theory of monads", J. Pure Appl. Algebra 2 (1972), p. 149-168. | Article | MR 299653 | Zbl 0241.18003

[52] R. Street, "Absolute colimits in enriched categories", Cahiers Topologie Géom. Différentielle 24 (1983), p. 377-379. | EuDML 91335 | Numdam | MR 749468 | Zbl 0532.18001

[53] R. Street, "Categorical structures", in Handbook of algebra, Vol. 1, North-Holland, 1996, p. 529-577. | Article | MR 1421811 | Zbl 0854.18001

[54] R. Street, "Frobenius monads and pseudomonoids", J. Math. Phys. 45 (2004), p. 3930-3948. | Article | MR 2095680 | Zbl 1071.18006

[55] R. Street, Quantum groups, Australian Mathematical Society Lecture Series, vol. 19, Cambridge Univ. Press, 2007. | MR 2294803 | Zbl 1117.16031

[56] K. Szlachányi - "Fiber functors, monoidal sites and Tannaka duality for bialgebroids", preprint arXiv:0907.1578, 2009.

[57] D. Verity - "Enriched categories, internal categories and change of base", Repr. Theory Appl. Categ. 20 (2011). | MR 2844536 | Zbl 1254.18001

[58] T. Wedhorn - "On Tannakian duality over valuation rings", J. Algebra 282 (2004), p. 575-609. | Article | MR 2101076 | Zbl 1088.18008

[59] J.-P. Wintenberger - "Un scindage de la filtration de Hodge pour certaines variétés algébriques sur les corps locaux", Ann. of Math. 119 (1984), p. 511-548. | Article | MR 744862 | Zbl 0599.14018