Shadows and traces in bicategories

Adams, J.F.: Prerequisites (on equivariant stable homotopy) for Carlsson’s lecture. In: Algebraic topology, Aarhus (1982). (Aarhus 1982), Lecture Notes in Mathematics, vol. 1051, pp. 483–532. Springer, Berlin (1984)

Baez, J.C., Dolan, J.: Higher-dimensional algebra. III. $$n$$ -categories and the algebra of opetopes. Adv. Math. 135(2), 145–206 (1998)

Bénabou, J.: Introduction to bicategories. In: Reports of the Midwest Category Seminar, pp. 1–77. Springer, Berlin (1967)

Brown, R.F.: The Lefschetz fixed point theorem. Scott, Foresman and Co., Glenview (1971)

Day, B., Street, R.: Monoidal bicategories and Hopf algebroids. Adv. Math. 129(1), 99–157 (1997)

tom Dieck, T.: Transformation groups, de Gruyter Studies in Mathematics, vol. 8. Walter de Gruyter & Co., Berlin (1987)

Dold, A.: The fixed point index of fibre-preserving maps. Invent. Math. 25, 281–297 (1974)

Dold, A., Puppe, D.: Duality, trace, and transfer. In: Proceedings of the International Conference on Geometric Topology (Warsaw, 1978), pp. 81–102. PWN, Warsaw (1980)

Freyd, P.J., Yetter, D.N.: Braided compact closed categories with applications to low-dimensional topology. Adv. Math. 77(2), 156–182 (1989)

Hasegawa, M.: The uniformity principle on traced monoidal categories. Publ. Res. Inst. Math. Sci. 40(3), 991–1014 (2004). http://projecteuclid.org/getRecord?id=euclid.prims/1145475500

Hattori, A.: Rank element of a projective module. Nagoya Math. J. 25, 113–120 (1965)

Jiang, B.J.: Lectures on Nielsen Fixed Point Theory, Contemporary Mathematics, vol. 14. American Mathematical Society, Providence (1983)

Joyal, A., Street, R.: The geometry of tensor calculus. II. Draft available at http://www.math.mq.edu.au/street/GTCII.pdf

Joyal, A., Street, R.: Planar diagrams and tensor algebra. Draft available at http://www.math.mq.edu.au/street/PlanarDiags.pdf

Joyal, A., Street, R.: The geometry of tensor calculus. I. Adv. Math. 88(1), 55–112 (1991)

Joyal, A., Street, R.: Braided tensor categories. Adv. Math. 102(1), 20–78 (1993)

Joyal, A., Street, R., Verity, D.: Traced monoidal categories. Math. Proc. Cambridge Philos. Soc. 119(3), 447–468 (1996)

Kelly, G.M., Laplaza, M.L.: Coherence for compact closed categories. J. Pure Appl. Algebra 19, 193–213 (1980)

Kelly, G.M., Street, R.: Review of the elements of $$2$$ -categories. In: Category Seminar (Proc. Sem., Sydney, 1972/1973), Lecture Notes in Mathematics, vol. 420, pp. 75–103. Springer, Berlin (1974)

Lewis Jr., L.G., May, J.P., Steinberger, M., McClure, J.E.: Equivariant stable homotopy theory, Lecture Notes in Mathematics, vol. 1213. Springer-Verlag, Berlin (1986). With contributions by J. E. McClure

May, J.P.: The additivity of traces in triangulated categories. Adv. Math. 163(1), 34–73 (2001)

May, J.P., Sigurdsson, J.: Parametrized Homotopy Theory, Mathematical Surveys and Monographs, vol. 132. American Mathematical Society, Providence (2006)

McCurdy, M.: Strings and stripes: graphical calculus for monoidal functors and monads http://web.science.mq.edu.au/mmccurdy/cms2010talk.pdf (2010). Talk at CMS meeting in Fredricton, NB

McCurdy, M.B.: Graphical methods for tannaka duality of weak bialgebras and weak hopf algebras in arbitrary braided monoidal categories. arXiv:1110.5542

Penrose, R.: Applications of negative dimensional tensors. In: Combinatorial Mathematics and its Applications (Proc. Conf., Oxford, 1969), pp. 221–244. Academic Press, London (1971)

Penrose, R., Rindler, W.: Spinors and space-time. vol. 1. Cambridge Monographs on Mathematical Physics. Cambridge University Press, Cambridge (1984). Two-spinor calculus and relativistic fields

Ponto, K.: Coincidence invariants and higher Reidemeister traces. arXiv:1209.3710

Ponto, K.: Equivariant fixed point theory. arXiv:0910.1274

Ponto, K.: Fixed point theory and trace for bicategories. Astérisque (333), xii+102 (2010). arXiv:0807.1471

Ponto, K.: Relative fixed point theory. Algebr. Geom. Topol. 11(2), 839–886 (2011). doi: 11110.2140/agt.2011.11.839 . http://dx.doi.org/10.2140/agt.2011.11.839

Ponto, K., Shulman, M.: Duality and trace in indexed monoidal categories. Submitted. Available online at http://www.math.ucsd.edu/mshulman/papers/indexed-color.pdf

Ponto, K., Shulman, M.: The multiplicativity of fixed point invariants. arXiv:1203.0950

Ranicki, A.: The algebraic theory of surgery. II. Applications to topology. Proc. London Math. Soc. (3) 40(2), 193–283 (1980)

Selinger, P.: A survey of graphical languages for monoidal categories. In: B. Coeke (ed.) New Structures for Physics, chap. 4. Springer, Berlin (2011). Available at http://www.mscs.dal.ca/selinger/papers.html#graphical . arXiv:0908.3347

Shulman, M.: Constructing symmetric monoidal bicategories. arXiv:1004.0993

Shulman, M.: Framed bicategories and monoidal fibrations. Theory Appl. Categ. 20(18), 650–738 (electronic) (2008). arXiv:0706.1286

Stallings, J.: Centerless groups—an algebraic formulation of Gottlieb’s theorem. Topology 4, 129–134 (1965)

Street, R.: Limits indexed by category-valued $$2$$ -functors. J. Pure Appl. Algebra 8(2), 149–181 (1976)

Street, R.: Low-dimensional topology and higher-order categories I. In: Proceedings of CT95, Halifax (1995). Available at http://www.mta.ca/cat-dist/CT95Docs/LowDim.ps

Street, R.: Categorical structures. In: Handbook of algebra, vol. 1, pp. 529–577. North-Holland, Amsterdam (1996). doi: 10.1016/S1570-7954(96),80019-2 . http://dx.doi.org/10.1016/S1570-7954(96)80019-2