Maths - Groups Objects

So far, we have defined a group as a set+structure, here we want to use the same structure but on top of other types of categories, so instead of defining a group in terms of its internal elements we define it in terms of its external properties, that is structure preserving mappings called functors (this is the category theory approach see this page).

To do this we take the structure in terms in the group identities:

and we put this in category theory terms:

We define:

and now define the identities in these terms:

Group Associativity

μ(a,μ(b,c)) = μ(μ(a,b),c)

μ(id×μ)(a,b,c) = μ(μ×id)(a,b,c)

μ(id×μ) = μ(μ×id)

group associativity
Group Identity μ(a,a-1) = e group identity
Group Inverse   group inverse


metadata block
see also:
Correspondence about this page

Book Shop - Further reading.

Where I can, I have put links to Amazon for books that are relevant to the subject, click on the appropriate country flag to get more details of the book or to buy it from them.

flag flag flag flag flag flag Symmetry and the Monster - This is a popular science type book which traces the history leading up to the discovery of the largest symmetry groups.

Terminology and Notation

Specific to this page here:


This site may have errors. Don't use for critical systems.

Copyright (c) 1998-2023 Martin John Baker - All rights reserved - privacy policy.