From: jim Date: Fri, 20 Mar 2015 12:44:03 +0000 (-0400) Subject: markup X-Git-Url: http://lambda.jimpryor.net/git/gitweb.cgi?p=lambda.git;a=commitdiff_plain;h=26ac7c6b289350fb981a197cfafe311dbc028247 markup --- diff --git a/topics/week7_introducing_monads.mdwn b/topics/week7_introducing_monads.mdwn index 2403da77..cb32a5e9 100644 --- a/topics/week7_introducing_monads.mdwn +++ b/topics/week7_introducing_monads.mdwn @@ -141,7 +141,7 @@ has to obey the following Map Laws: Essentially these say that `map` is a homomorphism from the algebra of `(universe Î± -> Î², operation â, elsment id)` to that of `(Î± -> Î², â', id')`, where `â'` and `id'` are `â` and `id` restricted to arguments of type `_`. That might be hard to digest because it's so abstract. Think of the following concrete example: if you take a `Î± list` (that's our `Î±`), and apply `id` to each of its elements, that's the same as applying `id` to the list itself. That's the first law. And if you apply the composition of functions `g â f` to each of the list's elements, that's the same as first applying `f` to each of the elements, and then going through the elements of the resulting list and applying `g` to each of those elements. That's the second law. These laws obviously hold for our familiar notion of `map` in relation to lists. - > As mentioned at the top of the page, in Category Theory presentations of monads they usually talk about "endofunctors", which are mappings from a Category to itself. In the uses they make of this notion, the endofunctors combine the role of a box type `_` and of the `map` that goes together with it. + > As mentioned at the top of the page, in Category Theory presentations of monads they usually talk about "endofunctors", which are mappings from a Category to itself. In the uses they make of this notion, the endofunctors combine the role of a box type `_` and of the `map` that goes together with it. * ***MapNable*** (in Haskelese, "Applicatives") A Mappable box type is *MapNable*