§ Quantifiers as adjoints

§ A first try: direct image, find right adjoint

     T
   t t t
   t t t
    |
    v
---tttt---- π(T)
-zzzzzzzzz--Z

§ Direct image, left adjoint

     T
   t t t
   t t t
    |
    v
---tttt---- π(T)
----zz--------Z

§ Inverse image, left adjoint.

    S
    -
    -   
   tttt
   tztt
   tztt T
   tztt
    ^^
    || π*(Z)
----zz-------Z