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Re: [Axiom-developer] "has" and "with" (was curious algebra failure)
From: |
Gabriel Dos Reis |
Subject: |
Re: [Axiom-developer] "has" and "with" (was curious algebra failure) |
Date: |
13 Aug 2007 11:50:19 -0500 |
William Sit <address@hidden> writes:
| I think I understand the objection raised by Gaby. In matching Monad to
| SetCategory with ..., Axiom is applying a forgetful functor that, given a
| monad, forgets all of its operations except those featured in SetCategory with
| .... In this sense, applying a forgetful functor is a form of automatic
| coercion on the level of categories. Gaby is correct in saying that strictly
| speaking, the forgetful functor should also not be automatic, just like the
| usual coercion between domains. In fact, how one forgets the structure of a
| ring to the structure of a Monad would be ambiguous, since there are two
| possible ways. For more complicated algebraic structures (like Hopf algebra,
| differential algebra) if it is possible to specify precisely the forgetful
| functor, it would allow us to have only one Monoid structure instead of an
| AbelianMonoid and a Monoid (and many others distinguished by different names
| for the monoid operation).
|
| Gaby, is that a fair statement?
Yes, that is close.
| You may be interested in this old 1986 article by Kamal Abdali et al., on An
| Object Oriented Approach to Algebra System Design:
|
| http://portal.acm.org/ft_gateway.cfm?id=32444&type=pdf&coll=GUIDE&dl=ACM
|
| One of the stated features of Views is:
|
| "Views do not depend on operation names. That is, locally (i.e. in their
| domains) two different Rings may have different names for their 'additon
| operation', but, when viewed as Rings, their addition operation is accessed by
| the same identifier."
Thanks; I had a copy, but I did not get back to it.
-- Gaby
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), (continued)
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Bill Page, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Bill Page, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), William Sit, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/12
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Bill Page, 2007/08/13
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/13
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Bill Page, 2007/08/13
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), William Sit, 2007/08/13
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure),
Gabriel Dos Reis <=
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Ralf Hemmecke, 2007/08/13
- [Axiom-developer] "has" and "with" and bug, Ralf Hemmecke, 2007/08/13
- Re: [Axiom-developer] "has" and "with" and bug, William Sit, 2007/08/13
- Re: [Axiom-developer] "has" and "with" and bug, Ralf Hemmecke, 2007/08/13
- [Axiom-developer] Re: "has" and "with" and bug, Gabriel Dos Reis, 2007/08/13
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/13
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Bill Page, 2007/08/13
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/13
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Ralf Hemmecke, 2007/08/13
- Re: [Axiom-developer] "has" and "with" (was curious algebra failure), Gabriel Dos Reis, 2007/08/13