Question

does anyone know about algebraic simplices?

Answer 1

sure

Answer 2

what exactly do you wan't to know. I may be able to help.

Answer 3

Also, I assume you mean simplicies in reference to algebraic topology. I am not sure what an algebraic simplicity is per se.

Answer 4

simplex*

Answer 5

in algebraic geometry and homological algebra

Answer 6

plural is simplices

Answer 7

I know about homology

Answer 8

I was correcting myself

Answer 9

oh. well i have been researching homological algebra and came to simplices and I would like to know more about them

Answer 10

well, there is much to know. So do you want to know how to find homology groups for spaces built out of simplicies?

Answer 11

also I have developed a theory of prime state algebraic logic, and was wondering if i could use simplices to extend my research

Answer 12

Simplices are good to compute things. Like you have some space and you want to triangulate it in order to figure out certain invariants. So if you need to compute something (homology for instance) they are great. There are many forms as well. Some have lax rules and are easier to work with but not as rich in theory.... So in short, be more specific :)

Answer 13

Munkres and Hatcher both have great books about algebraic topology (this is where the idea of a simplex started).

Answer 14

I am trying use category theory to prove that simplices are isomorphic to multi-dimensional spheres

Answer 15

Do you know what homotopy is?

Answer 16

What does isomorphism mean in terms of a general category?

Answer 17

i have come across the term, but I am not very familiar with it yet

Answer 18

by isomorphic, i mean there exists some map from the category of simplices to the category of spheres that is both an epimorphism and a monomorphism

Answer 19

also, what is the difference between a functor and a morphism?

Answer 20

I see a n-simplex as being homeotopic to a n-sphere. Which means we can "stretch" one into the other. So I am guessing your question is the same thing. But when you say a function from the catagory you lost me.

Answer 21

do you know anything about category theory?

Answer 22

I know about rings groups and fields

Answer 23

But when you say a function from the category of simplices to the category of n-spheres then the domain is a set of n-simplices and I am not sure of the operation...

Answer 24

there is no great difference between functors an morphisms. Functors are homomorphisms on categories. Morphism just means structure preserving and so depending on the structure you are preserving...

Answer 25

i see. In the book i am reading, there was an entire chapter devoted to category theory. I have found a way to determine uniquely a multi-dimensional sphere with a set of linearly independent points. these points can also be thought of as the vertices of a homological simplex.

Answer 26

yes for sure. The convex hull of your linearly independent points