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 [math]\displaystyle{ \mathcal{V} }[/math] be a symmetric monoidal closed category, and let [math]\displaystyle{ \mathcal{A} }[/math] be a small category enriched in [math]\displaystyle{ \mathcal{V} }[/math].
The Isbell conjugacy is an adjunction between the categories [math]\displaystyle{ \mathcal{V}^{\mathcal{A}^{op}} }[/math] and [math]\displaystyle{ (\mathcal{V}^{\mathcal{A}})^{op} }[/math] arising from the Yoneda embedding [math]\displaystyle{ Y:\mathcal{A}\rightarrow\mathcal{V}^{\mathcal{A}^{op}} }[/math] and the dual Yoneda embedding [math]\displaystyle{ Z:\mathcal{A}\rightarrow(\mathcal{V}^{\mathcal{A}})^{op} }[/math].
References
- ↑ "Taking categories seriously", Revista Colombiana de Matemáticas 20 (3–4): 147–178, 1986, http://eudml.org/doc/181771
Bibliography
- {{citation
| last = Kelly | first = Gregory Maxwell | isbn = 0-521-28702-2 | mr = 651714 | publisher = Cambridge University Press, Cambridge-New York | series = London Mathematical Society Lecture Note Series | title = Basic concepts of enriched category theory | volume = 64
- Day, Brian J.; Lack, Stephen (2007), "Limits of small functors", Journal of Pure and Applied Algebra 210 (3): 651–663, doi:10.1016/j.jpaa.2006.10.019.
 |
