My homepage | My math page | My math news (old archive, old archive in RSS) | Donate for the research
2005-07-19 11:31
Category theory news - described category of classes and objects
.
I developed a theory of objects and classes
. It is an abstract
math theory which describes classes
, a generalization of n-ary
relations. Classes have come to abstract mathematics from computer science
but now they are found the place to be abstract math natives
.
Read here (draft but quite readable).
A thing I called classes with argument and result
describe
dependency of Y from X. Classes with argument and result form an
interesting category (in the sense of
category
theory).
There are some interesting things here:
The theory of classes may be considered as a generalization of universal algebra (and theory of models in general) taking the place between category theory and universal algebra, which was missing in mathematics. On the other hand, classes may be probably considered even as a generalization (!) of category theory.
(The research of relations between theory of objects and classes and universal algebra and category theory is not yet done, but it surely will produce interesting results.)
I defined epi-, mono-, and isomorphisms for the category of classes but I have not yet checked that these definitions agree with category theory. So we have a yet open problem (however looking simple) to solve (prove that these are really epi-, mono- and isomorphisms). I'm looking for a solution.
I defined homomorphism algebraically. As I've said above, it seems to be a generalization of universal algebra. So we have started algebraization of algebra. (Other fields of math were algebraized, but what's about algebra itself?)
I have given formal definitions to X (argument) and Y (result). They were formerly unknown and so I discovered them :-)
Finally, I believe that X (argument
) in my theory is Father,
Y (result
) is Son, and index
is Holy Spirit.
Related categories:
Keywords: category theory, universal algebra, n-ary relation, fundamental computer science, model theory, science and religion, religion and science, science and Christianity, Christianity and science, math news, mathematical news, mathematics, math, mathematicians, science news, computer science, informatics, science
News listing generated with Rich RSS2HTML TM 0.2.1 (original).