User:Michiexile/MATH198/Lecture 5
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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.
Limits and colimits
- Generalizing these constructions
- Diagram and universal object mapping to (from) the diagram
- Express product/coproduct as limit/colimit
- Issues with Haskell
- No dependent types
- No compiler-enforced equational conditions
- Can be simulated but not enforced, e.g. using QuickCheck.
Useful limits and colimits
Equalizer, coequalizer
- Kernels, cokernels, images, coimages
- connect to linear algebra: null spaces et.c.
Pushout and pullback squares
- Computer science applications