Thanks for the comments. Zack Luo -----Original Message----- From: Peter Selinger [mailto:selinger@mathstat.dal.ca] Sent: Monday, December 10, 2007 8:22 PM To: Zhaohua Luo Subject: Re: categories: new website: clones and genoids By "itself", do you mean A or G? Grammatically, I would understand "the product of A with itself" to be A x A, but then your definition does not have the stated consequences. I therefore assume that you meant "the product of A with G". Another unambiguous way to express this is "G is the product of itself with A". -- Peter Zhaohua Luo wrote:
A genoid is a category of only two objects (A, G) such that G is the
product
of A with itself (thus G is also the product of any finite power of A with itself). It is a remarkable fact that such a simple concept can be used to define all of the fundamental algebraic theories, including lambda calculus and first order logic. Progress made in this direction is presented at a newly created website entitled "Clones <http://www.algebraic.net/cag> and Genoids" (http://www.algebraic.net/cag).
Zhaohua Luo