Isbell conjugacy

Isbell conjugacy (named after John R. Isbell) is a fundamental construction of enriched category theory formally introduced by William Lawvere in 1986.[1]

Definition

Let be a symmetric monoidal closed category, and let be a small category enriched in .

The Isbell conjugacy is an adjunction between the categories and arising from the Yoneda embedding and the dual Yoneda embedding .

References

  1. Lawvere, F. W. (1986), "Taking categories seriously", Revista Colombiana de Matemáticas, 20 (3–4): 147–178, MR 0948965

Bibliography

  • Kelly, Gregory Maxwell (1982), Basic concepts of enriched category theory, London Mathematical Society Lecture Note Series, 64, Cambridge University Press, Cambridge-New York, ISBN 0-521-28702-2, MR 0651714.
  • Day, Brian J.; Lack, Stephen (2007), "Limits of small functors", Journal of Pure and Applied Algebra, 210 (3): 651–663, arXiv:math/0610439, doi:10.1016/j.jpaa.2006.10.019, MR 2324597.


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