Difference between revisions of "User:Michiexile/MATH198/Lecture 7"

From HaskellWiki
Jump to navigation Jump to search
 
Line 1: Line 1:
 
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.
  
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)
  +
  +
  +
===Why should we care in CS?===
  +
  +
====Monads====

Revision as of 22:20, 29 October 2009

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)


Why should we care in CS?

Monads

Retrieved from "https://wiki.haskell.org/index.php?title=User:Michiexile/MATH198/Lecture_7&oldid=31340"