Re: [Haskell-cafe] N and R are categories, no?

2007-03-16 Thread Jules Bean
Dominic Steinitz wrote: I haven't formally checked it, but I would bet that this endofunctor over N, called Sign, is a monad: Just to be picky a functor isn't a monad. A monad is a triple consisting of a functor and 2 natural transformations which make certain diagrams commute. Whi

Re: [Haskell-cafe] N and R are categories, no?

2007-03-15 Thread Nicolas Frisby
Thanks for keeping me honest ;) On 3/15/07, Dominic Steinitz <[EMAIL PROTECTED]> wrote: > I haven't formally checked it, but I would bet that this endofunctor > over N, called Sign, is a monad: Just to be picky a functor isn't a monad. A monad is a triple consisting of a functor and 2 natural t

Re: [Haskell-cafe] N and R are categories, no?

2007-03-15 Thread Dominic Steinitz
> I haven't formally checked it, but I would bet that this endofunctor > over N, called Sign, is a monad: Just to be picky a functor isn't a monad. A monad is a triple consisting of a functor and 2 natural transformations which make certain diagrams commute. If you are looking for examples, I al

Re: [Haskell-cafe] N and R are categories, no?

2007-03-15 Thread Nicolas Frisby
That said, N and R are indeed categories; however, considering them as categories should be carefully interlaced with your intuitions about them as types. I haven't formally checked it, but I would bet that this endofunctor over N, called Sign, is a monad: Sign x = x + x Pos = injectLeft Neg

Re: [Haskell-cafe] N and R are categories, no?

2007-03-15 Thread Ulf Norell
On 3/15/07, Steve Downey <[EMAIL PROTECTED]> wrote: EOk, i'm trying to write down, not another monad tutorial, because I don't know that much yet, but an explication of my current understanding of monads. But before I write down something that is just flat worng, I thought I'd get a cross check

[Haskell-cafe] N and R are categories, no?

2007-03-14 Thread Steve Downey
EOk, i'm trying to write down, not another monad tutorial, because I don't know that much yet, but an explication of my current understanding of monads. But before I write down something that is just flat worng, I thought I'd get a cross check. (and I can't get to #haskell) Monads are Functors.