Nottingham FP Lab Blog

FP lunch 25 May

by Thorsten on May 25, 2007.
Tagged as: Lunches.

Lots of people away. I used the occassion to give an educational introduction to my latest obsession: classifying functors by the limits they preserve. The list functor preserves pullbacks, and indeed I showed on the whiteboard that all containers preserve pullbacks. The question: do you know a functor that does not preserve pullbacks created some silence, which i used to finish my sandwhich. I then pulled out my two favorite examples: the continuation functor $F X = (X \to R) \to R$ and the unordered pair functor $P X = X\times X / \sim$ where $(x,y)\sim(x,y)$ and $(x,y)\sim(y,x)$ and not wanting to bore the audience too much, I handwaved an explanation why unordered pairs do neither preserve pullbacks nor equalizers. The question remains what do the preserve and why are they more civilized than continuations…