The formal theory of Tannaka duality

Schäppi, Daniel

Astérisque, no. 357 (2013) , 148 p.

MR Zbl

@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},
     mrnumber = {3185459},
     zbl = {1314.18008},
     language = {en},
     url = {http://archive.numdam.org/item/AST_2013__357__R1_0/}
}

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%A Schäppi, Daniel
%T The formal theory of Tannaka duality
%S Astérisque
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Schäppi, Daniel. The formal theory of Tannaka duality. Astérisque, no. 357 (2013), 148 p. http://numdam.org/item/AST_2013__357__R1_0/

Bibliographie
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[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. | MR | Zbl | DOI

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

[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 | Zbl

[5] A. Bruguières - "On a Tannakian theorem due to Nori", unpublished, available on http://www.math.univ-montp2.fr/~bruguieres/ (July 10, 2011), 2004.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

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

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

[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

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

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

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

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

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

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

[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. | Zbl | MR | DOI

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

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

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

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

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

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

[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. | MR | Zbl | DOI

[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. | Zbl | MR

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

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

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

[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. | MR | Zbl | DOI

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

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

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

[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. | MR | Zbl | DOI

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

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

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

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

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

[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. | MR | Zbl | DOI

[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. | MR | Zbl | DOI

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

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

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

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

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

[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 | Zbl

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

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

[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. | MR | Zbl | DOI

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

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

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

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

[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). | Zbl | MR

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

[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. | MR | Zbl | DOI