Isbell conjugacy

Short description: Construction of enriched category theory

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

Definition

Let ${𝒱}$ be a symmetric monoidal closed category, and let ${𝒜}$ be a small category enriched in ${𝒱}$.

The Isbell conjugacy is an adjunction between the categories ${{𝒱}}^{{{𝒜}}^{op}}$ and $({{𝒱}}^{{𝒜}}{)}^{op}$ arising from the Yoneda embedding $Y:{𝒜}\to {{𝒱}}^{{{𝒜}}^{op}}$ and the dual Yoneda embedding $Z:{𝒜}\to ({{𝒱}}^{{𝒜}}{)}^{op}$.

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 .