John Baez:

“There must be hundreds of mathematicians roaming the earth thinking operads are difficult and abstruse, because they’ve seen the definition without any pictures.

These people should be grateful they weren’t taught how to tie their shoes in an equally wrong-headed manner.”

What is an operad?

  • A collection of  N→1 operators
  • “associatively composable”
  • permutable

Why should someone interested in homotopy care about operads?

  • the main way to probe a space is by looking at the maps from circle, sphere, 3-sphere, 4-sphere, … onto it.
  • “Most homotopy theorists would gladly sell their souls for the ability to compute the homotopy groups of an arbitrary space”
  • Operads organise the information of the restricted higher homotopies.
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