Abstract
Higher categories, that is, n-categories represent promising tools for multi-level complexity studies. Specific notions as, n-categories, periodic table, monoidal, braided, sylleptic, and symmetric categories, categorification and coherence are introduced.
Elements of synthetic differential geometry, SDG, and toposes are outlined.
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References
Baez, J.: An introduction to n-categories. In: Moggi, E., Rosolini, G. (eds.) CTCS 1997. LNCS, vol. 1290. Springer, Heidelberg (1997)
Baez, J.: Topos theory in a nutshell (2006), http://math.ucr.edu/home/baez/topos.html
Baez, J., Dolan, J.: Higher dimensional algebra and topological quantum field theory. Jour. Math. Phys. 36, 6073–6105 (1995)
Baez, J., Dolan, J.: Categorification. In: Getzler, E., Kapranov, M. (eds.) Higher Category Theory. Contemp Math., vol. 230, pp. 1–36. Amer. Math. Soc, Providence (1998)
Bell, J.L.: A Primer of Infinitesimal Analysis. Cambridge University Press, New York (1998)
Crans, S.: A tensor product for Gray categories. Theory and Applications of Categories 5(2), 12–69 (1999)
Crans, S.: On braidings, syllepses ans symmetries. Cahiers Topologie Geom ifferentielle Categ. 41(1), 2–74 (2000)
Goldblatt, R.: Topoi. The Categorical Analysis of Logic. North-Holland Publishing Theory, Amsterdam (1979)
Gordon, R., Power, A.J., Street, R.: Coherence for tricategories. Memoirs Amer. Math. Soc. 117(558) (1995)
Gurski, N.: An algebraic theory of tricategories. PhD thesis, University of Chicago, IL (2006)
Kelly, G.M., Street, R.: Review of the elements of 2-categories. Lecture Notes in Math. 420, 75–103 (1974)
MacLane, S.: Categories for the Working Mathematician. Springer, New York (1971)
Moerdijk, I., Reyes, G.E.: Models for Smooth Infinitesimal Analysis. Springer, New York (1991)
Leinster, T.: Higher Operads, Higher Categories. Cambridge University Press, Cambridge (2004)
Sheppeard, M.D.: Gluon Phenomenology and a Linear Topos. Ph, D Thesis Univ. of Canterbury, New Zeeland (2007)
Street, R.: The algebra of oriented simplexes. J. Pure Appl. Algebra. 49, 283–335 (1987)
Street, R.: Categorical and combinatorial aspects of descent theory. Applied Categorical Structures 12, 537–576 (2004)
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Iordache, O. (2011). Category Theory. In: Modeling Multi-Level Systems. Understanding Complex Systems, vol 70. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17946-4_14
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DOI: https://doi.org/10.1007/978-3-642-17946-4_14
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