You can handwave equality, but you need to specify which equality. same with "isomorphism". same form or equal form? how is the equality specified there? canoni

You can handwave equality, but you need to specify which equality. same with "isomorphism". same form or equal form? how is the equality specified there? canonical has a precise definition, but the paper doesn't come close. eg array-equal as in lisp, vs eqc vs equal vs eq. list of atoms with the same order and same values. or list of equal atoms. (ie same pointers). or if the values are same, or all the other atom properties need to be the same. without a precise definition of equality everything is just handwaving. in perl "" equals 0 equals !!0. so are they equal, and if so which equality? same with JavaScript, python and PHP with completely handwave equality definitions. in the end it all comes to Greenspun, all the lisp equalities. Grothendiek is lucky to ignore pointers. for him all natural numbers can be equal. 1 === 1. for us eg with python higher numbers with the same value are sometimes not eq. This would have driven Grothendiek even more nuts.