To All, A few thoughts about the "evilness" of equality. There is a well established doctrine, possibly going back to Felix Klein, that mathematical reality should be described in invariant terms. For examples, many aspects of the theory of vector spaces can be developed independantly of the choice of a basis. The fact that the (in)equality relation between the objects of a category is not respected by equivalences of categories can be disturbing. By loosing its invariance, the relation seems to be loosing its objectivity, its value. This is why some category theorists have declared war on it by calling it "evil". The cardinality of the set of objects of a category is not invariant under equivalences. Similarly, the cardinality of the set of points of a topological space is not invariant under homotopy equivalences. Where is the problem? Best, andré -------- Message d'origine-------- De: JeanBenabou [mailto:jean.benabou@wanadoo.fr] Date: dim. 12/09/2010 08:38 À: David Leduc Cc: categories Objet : categories: Re: Evil in bicategories Dear all, Although I'm not a very "religious" person, I respect all religions, and I also deeply respect, of course, Category Theory. I hope someone will answer the following question: Is Category Theory a religion? As far as I know, it is the only part of mathematics (or of many other sciences) where words such as "dogma", "doctrine" (let alone hyper ones) are used. Recently a few other words with the same religious connotation have been added. The most frequent one being "evil" Maybe my english isn't so "beautiful", but in all cases where "evil" has been used, what is wrong with "wrong" instead? [For admin and other information see: http://www.mta.ca/~cat-dist/ ]