Following up on Paul Taylor's suggestion to " ... play around with skeletons, bones or even the Grim Reaper ... ", Vaughan Pratt <pratt@cs.stanford.edu> offered:
... how about "scythe" for the functor [-,1+1]: C^op --> C? In a Boolean topos this is just the (internal) contravariant power object functor, but more generally it tends to cleave objects into their connected components in a suitable sense.
But "scythe"? A scythe is for cutting off stalks, wholesale. (A sickle is for cutting them off ... umm ... retail, perhaps :-) .) To "cleave" an object in two one might utilize a *cleaver*, or, more bluntly, a *wedge* -- but the resulting two parts are probably *not* in most instances "connected" at all, let alone "connected components": rather, they merely provide a binary coproduct decomposition of the given object. Cheers, -- Fred [For admin and other information see: http://www.mta.ca/~cat-dist/ ]