nLab
two-variable adjunction
Idea
An adjunction of two variables is a straightforward generalization of both:
by extracting the central pattern.
Definition
Let , and be categories. An adjunction of two variables or two-variable adjunction
(\otimes, hom_l, hom_r) : C \times D \to E
consists of functors
\begin{aligned}
\otimes & : C \times D \to E
\\
hom_l &: C^{op} \times E \to D
\\
hom_r &: D^{op} \times E \to C
\end{aligned}
together with natural isomorphisms
Hom_E(C \otimes D, E)
\simeq
Hom_C(D, hom_l(C,E))
\simeq
Hom_D(C, hom_r(D,E))
\,.
References
This is in chapter 4 of
- Mark Hovey. Model Categories, volume 63 of Mathematical Surveys and Monographs. American Mathematical Society, 1999.
Revised on January 8, 2009 22:48:48
by
Toby Bartels
(71.104.234.95)