Frobenius algebras and ambidextrous adjunctions

Theory and Applications of Categories

Volumn 16, Issue 4, 2006, Pages 84-122

  Lauda, Aaron D ^a  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

Author keywords

Eilenberg Moore completion; Frobenius pseudomonoid; Pseudoadjunction; Pseudomonad

Indexed keywords

EID: 33646423030     PISSN: 1201561X     EISSN: 1201561X     Source Type: Journal    
DOI: None     Document Type: Article

References (38)

1. Lowell Abrams. Two-dimensional topological quantum Held theories and Frobenius algebras. J. Knot Theory Ramifications, 5, 1996.
2. Michael Atiyah. Topological quantum field theories. Inst. Hautes Études Sci. Publ. Math.
3. John C. Baez. This week's finds in mathematical physics. Available at http://www.math.ucr.edu/home/baez/week174.html.
4. G. J. Bird, G. M. Kelly, A. J. Power, and R. H. Street. Flexible limits for 2-categories. J. Pure Appl. Algebra, 61, 1989.
5. R. Blackwell, G. M. Kelly, and A. J. Power. Two-dimensional monad theory. J. Pure Appl. Algebra, 59, 1989.
6. Francis Borceux. Handbook of categorical algebra. 2, volume 51 of Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge, 1994. Categories and structures.
7. Brian Day and Ross Street. Monoidal bicategories and Hopf algebroids. Adv. Math., 129, 1997.
8. Brian Day and Ross Street. Quantum categories, star autonomy, and quantum groupoids. In Galois theory, Hopf algebras, and semiabelian categories, volume 43 of Fields Inst. Commun., pages 187-225. Amer. Math. Soc., Providence, RI, 2004.
9. Robbert Dijkgraaf. A geometric approach to two dimensional conformal field theory. PhD thesis, University of Ultrecht, 1989. Available electronically as hep-th/9703136.
10. Samuel Eilenberg and John C. Moore. Adjoint functors and triples. Illinois J. Math., 9:381-398, 1965.
11. Roger Godement. Topologie algébrique et théorie des faisceaux. Actualities Sci. Ind. No. 1252. Publ. Math. Univ. Strasbourg. No. 13. Hermannm Paris, 1958.
12. R. Gordon, A. J. Power, and R. Street. Coherence for tricategories. Memoirs of the American Mathematical Society, 117(558), 1995.
13. John W. Gray. Formal category theory: adjointness for 2-categories. Springer-Verlag, Berlin, 1974. Lecture Notes in Mathematics, Vol. 391.
14. André Joyal and Ross Street. The geometry of tensor calculus. I. Adv. Math., 88, 1991.
15. Lars Kadison. New examples of Frobenius extensions, volume 14 of University Lecture Series. American Mathematical Society, Providence, RI, 1999.
16. G. M. Kelly. Structures defined by finite limits in the enriched context. I. Cahiers Topologie Géom. Différentielle, 23:3-42, 1982. Third Colloquium on Categories, Part VI (Amiens, 1980).
17. G. M. Kelly and Ross Street. Review of the elements of 2-categories. In Category Seminar, volume 420 of Springer Lecture Notes in Mathematics, pages 75-103, 1974.
18. Gregory M. Kelly, editor. Category Seminar. Springer-Verlag, Berlin, 1974. Lecture Notes in Mathematics, Vol. 420.
19. Gregory Maxwell Kelly. Basic concepts of enriched category theory, volume 64 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1982. Also in Reprints in Theory and Applications of Categories 10
20. Mikhail Khovanov. A functor-valued invariant of tangles. Algebr. Geom. Topol., 2:665-741 (electronic), 2002.
21. H. Kleisli. Every standard construction is induced by a pair of adjoint functors. Froc. Amer. Math. Soc., 16:544-546, 1965.
22. Joachim Kock. Frobenius Algebras and 2D Topological Quantum Field Theories, volume 59 of London Mathematical Society Student Text. Cambridge University Press, Cambridge, 2004.
23. Stephen Lack. A coherent approach to pseudomonads. Adv. Math., 152, 2000.
24. Stephen Lack and Ross Street. The formal theory of monads. II. J. Pure Appl. Algebra, 175, 2002. Special volume celebrating the 70th birthday of Professor Max Kelly.
25. Aaron Lauda. Frobenius algebras and ambidextrous adjunctions. Available electronically as math.CT/0502550, 2005.
26. Aaron D. Lauda. Frobenius algebras and planar open string topological field theories. Available electronically as math.QA/0508349, 2005.
27. F. William Lawvere. Ordinal sums and equational doctrines. In Sem. on Triples and Categorical Homology Theory (ETH, Züich, 1966/67), pages 141-155. Springer, Berlin, 1969.
28. Saunders Mac Lane. Homologie des anneaux et des modules. In Colloque de topologie algébrique, Louvain, 1956, pages 55-80. Georges Thone, Liège, 1957.
29. F. Marmolejo. Doctrines whose structure forms a fully faithful adjoint string. Theory Appl. Categ., 3:No. 2, 24-44 (electronic), 1997.
30. F. Marmolejo. Distributive laws for pseudomonads. Theory Appl. Categ., 5:No. 5, 91-147 (electronic), 1999.
31. Michael Müger. From subfactors to categories and topology. I. Frobenius algebras in and Morita equivalence of tensor categories. J. Pure Appl. Algebra, 180, 2003.
32. Ross Street. The formal theory of monads. J. Pure Appl. Algebra, 2, 1972.
33. Ross Street, Fibrations and Yoneda's lemma in a 2-category. In Category Seminar (Proc. Sem., Sydney, 1972/1973), pages 104-133. Lecture Notes in Math., Vol. 420. Springer, Berlin, 1974.
34. Ross Street. Limits indexed by category-valued 2-functors. J. Pure Appl. Algebra, 8, 1976.
35. Ross Street. Low-dimensional topology and higher-order categories. In Proceedings of CT95, Halifax, July 9-15, 1995.
36. ROSS Street. Frobenius monads and pseudomonoids. J. Math. Phys., 45, 2004.
37. Ulrike Tillmann. S-structures for k-linear categories and the definition of a modular functor. J. London Math. Soc. (2), 58, 1998.
38. D. Verity. Enriched, Categories, Internal Categories, and Change of Base. PhD thesis, University of Cambridge. 1992. Available as Macquarie Mathematics Report 93-123.