User:Michiexile/MATH198/Lecture 8
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IMPORTANT NOTE: THESE NOTES ARE STILL UNDER DEVELOPMENT. PLEASE WAIT UNTIL AFTER THE LECTURE WITH HANDING ANYTHING IN, OR TREATING THE NOTES AS READY TO READ.
Some adjunctions we already know
- initial/terminal are adjunctions.
- (co)-products are adjunctions.
- Actually, all (co)limits are adjunctions.
Some adjunctions we don't know yet
- Existential and universal qualifiers as adjunctions.
- Powersets and im(f) -| f^\inv
Properties of adjoints
RAPL: Right Adjoints Preserve Limits
Recognizing adjoints
Theorem (Freyd: The Adjoint Functor Theorem)