I'm afraid my diagrams didn't commute very well, someone's mailer is eating the vertical-bar symbol. Here they are with ! in place of vertical bar. A category mailing list should be less rough on diagrams. b c -----------> ---------> ! ---------> ! ! ! b c ! b ! ! __ ! a! @ ------>------> = ! __ ! !a //! !a ! a! //! a! ! // ! ! ! // ! V c V V V V ---------> ---------> -----------> b c b c -----------> ---------> ! ---------> ! ! b c ! ! b ! ! // ! ------>------> @ a! = ! ! !a !// !a ! a! // a! ! -- ! ! ! !// ! V c V V V -- V ---------> ---------> -----------> b c -Vaughan Pratt