[Haskell-cafe] Re: Category Theory woes
Mark Spezzano mark.spezzano at chariot.net.au writes: Does anyone know what Hom stands for? 'Hom' stands for 'homomorphism' --a way of changing (morphism) between two structures while keeping some information the same (homo-). Any algebra text will define morphisms aplenty --homomorphisms, epimorphisms, monomorphisms, and the like. These are maps on groups that preserve group operations (or on rings that preserve ring operations, etc.) In a topology text, you will find information on what are called continuous functions; they're morphisms too, in disguise. You can find a thinner disguise when you look at continuously invertible continuous functions, which are called homeomorphisms. If you proceed to differential geometry, you'll see smooth maps --they're morphisms too, and the invertible ones are called diffeomorphisms. This-morphisms, that-morphisms --if you're trying to come up with a general theory that describes all of them, it's natural just to call them 'morphisms'; but, as with the word 'colonel', the word and the symbol come to us via different routes, so that 'Hom(omorphism)' survives instead as the abbreviation. The crucial point in learning category theory is the realisation that, despite all the fancy terminology, it is at heart nothing but a way of talking about groups, rings, topological spaces, partial orders, etc. --all at once, so no wonder it seems abstract! ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: Category Theory woes
On Tue, 02 Feb 2010 09:16:03 -0800, Creighton Hogg wrote: 2010/2/2 Álvaro García Pérez agar...@babel.ls.fi.upm.es You may try Pierce's Basic Category Theory for Computer Scientists or Awodey's Category Theory, whose style is rather introductory. Both of them (I think) have a chapter about functors where they explain the Hom functor and related topics. I think Awodey's book is pretty fantastic, actually, but I'd avoid Pierce. Unlike Types and Programming Languages, I think Basic Category Theory... is a bit eccentric in its presentation and doesn't help the reader build intuition. I have written an overview of various category theory books, which you may find useful, at the following site: Learning Haskell through Category Theory, and Adventuring in Category Land: Like Flatterland, Only About Categories http://dekudekuplex.wordpress.com/2009/01/16/learning-haskell-through-category-theory-and-adventuring-in-category-land-like-flatterland-only-about-categories/ Hope this helps. -- Benjamin L. Russell -- Benjamin L. Russell / DekuDekuplex at Yahoo dot com http://dekudekuplex.wordpress.com/ Translator/Interpreter / Mobile: +011 81 80-3603-6725 Furuike ya, kawazu tobikomu mizu no oto. -- Matsuo Basho^ ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
Re: [Haskell-cafe] Re: Category Theory woes
On Sun, 07 Feb 2010 01:38:08 +0900 Benjamin L. Russell dekudekup...@yahoo.com wrote: On Tue, 02 Feb 2010 09:16:03 -0800, Creighton Hogg wrote: 2010/2/2 Álvaro García Pérez agar...@babel.ls.fi.upm.es You may try Pierce's Basic Category Theory for Computer Scientists or Awodey's Category Theory, whose style is rather introductory. Both of them (I think) have a chapter about functors where they explain the Hom functor and related topics. I think Awodey's book is pretty fantastic, actually, but I'd avoid Pierce. Unlike Types and Programming Languages, I think Basic Category Theory... is a bit eccentric in its presentation and doesn't help the reader build intuition. I have written an overview of various category theory books, which you may find useful, at the following site: Learning Haskell through Category Theory, and Adventuring in Category Land: Like Flatterland, Only About Categories http://dekudekuplex.wordpress.com/2009/01/16/learning-haskell-through-category-theory-and-adventuring-in-category-land-like-flatterland-only-about-categories/ Hope this helps. It does. Does anybody have any opinions on Pitt, Category Theory and Computer Science ? Brian ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
[Haskell-cafe] Re: Category Theory woes
Mark Spezzano mark.spezzano at chariot.net.au writes: Maybe there are books on Discrete maths or Algebra or Set Theory that deal more with Hom Sets and Hom Functions? Googling haskell category theory I got: http://en.wikibooks.org/wiki/Haskell/Category_theory http://www.haskell.org/haskellwiki/Category_theory and many others. The latter has a list of books. Perhaps people could update with books they are familiar with and add comments? Dominic. ___ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
