Personal tools

User:Michiexile/MATH198/Lecture 8

From HaskellWiki

< User:Michiexile | MATH198(Difference between revisions)
Jump to: navigation, 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)
  +
  +
===Yoneda's Lemma===
  +
  +
===F-functors and algebraic data structures===

Revision as of 17:23, 4 November 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.

Contents

1 Some adjunctions we already know

  • initial/terminal are adjunctions.
  • (co)-products are adjunctions.
  • Actually, all (co)limits are adjunctions.


2 Some adjunctions we don't know yet

  • Existential and universal qualifiers as adjunctions.
  • Powersets and im(f) -| f^\inv

3 Properties of adjoints

3.1 RAPL: Right Adjoints Preserve Limits

3.2 Recognizing adjoints

Theorem (Freyd: The Adjoint Functor Theorem)

4 Yoneda's Lemma

5 F-functors and algebraic data structures