Skip to main content

Category Theory

  • Chapter
Modeling Multi-Level Systems

Part of the book series: Understanding Complex Systems ((UCS,volume 70))

  • 1309 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 149.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 199.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Baez, J.: An introduction to n-categories. In: Moggi, E., Rosolini, G. (eds.) CTCS 1997. LNCS, vol. 1290. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  • 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)

    Article  MATH  MathSciNet  Google Scholar 

  • 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)

    Google Scholar 

  • Bell, J.L.: A Primer of Infinitesimal Analysis. Cambridge University Press, New York (1998)

    MATH  Google Scholar 

  • Crans, S.: A tensor product for Gray categories. Theory and Applications of Categories 5(2), 12–69 (1999)

    MATH  MathSciNet  Google Scholar 

  • Crans, S.: On braidings, syllepses ans symmetries. Cahiers Topologie Geom ifferentielle Categ. 41(1), 2–74 (2000)

    MATH  MathSciNet  Google Scholar 

  • Goldblatt, R.: Topoi. The Categorical Analysis of Logic. North-Holland Publishing Theory, Amsterdam (1979)

    Google Scholar 

  • Gordon, R., Power, A.J., Street, R.: Coherence for tricategories. Memoirs Amer. Math. Soc. 117(558) (1995)

    Google Scholar 

  • Gurski, N.: An algebraic theory of tricategories. PhD thesis, University of Chicago, IL (2006)

    Google Scholar 

  • Kelly, G.M., Street, R.: Review of the elements of 2-categories. Lecture Notes in Math. 420, 75–103 (1974)

    Article  MathSciNet  Google Scholar 

  • MacLane, S.: Categories for the Working Mathematician. Springer, New York (1971)

    Google Scholar 

  • Moerdijk, I., Reyes, G.E.: Models for Smooth Infinitesimal Analysis. Springer, New York (1991)

    MATH  Google Scholar 

  • Leinster, T.: Higher Operads, Higher Categories. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

  • Sheppeard, M.D.: Gluon Phenomenology and a Linear Topos. Ph, D Thesis Univ. of Canterbury, New Zeeland (2007)

    Google Scholar 

  • Street, R.: The algebra of oriented simplexes. J. Pure Appl. Algebra. 49, 283–335 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  • Street, R.: Categorical and combinatorial aspects of descent theory. Applied Categorical Structures 12, 537–576 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

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

Download citation

Publish with us

Policies and ethics