Abstract: The talk will proceed from scratch - as all proper logical talks should, No big new theorems but, I think, a big new conjecture, illustrated by clear and surprising examples. I have given versions of this talk during the last 10 months twice - unfortunately, both times with limited success, mainly because of the time available being limited ... . The difficulty has nothing to do with prerequisites; it has to do with the presence or absence of "the logical interest" and willingness to pay attention. Let me try again to raise your interest in categorical logic.