FP lunch 25 May

May 25th, 2007 by Thorsten

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…

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