The word products is used not only for products of numbers, functions, matrices and so on (i.e., product as a binary operation) but also for products of various algebraic structures, spaces, products in category theory etc. If I understand correctly the tag-excerpt (created by Davide Giraudo, this tag is not for the "more abstract" products. The current version of the tag-excerpt looks like this:
For questions about the evaluation of finite products, or their properties. For infinite ones, use "infinite-products" tag.
However, if you look into this tag, at the moment you will find there many questions about products of topological spaces, groups, etc. (Just try to have a look at the questions tagged products+general-topology, products+group-theory, products+abstract-algebra, products+category-theory, products+measure-theory, etc.)
It is also worth mentioning that we also have tags product-space (for products of topological spaces and measure spaces, according to the tag description) and also separate tags for some constructions in group theory and abstract algebra - direct-product, semidirect-product, wreath-product.
So some of the questions which do not follow the tag description could be retagged, but for some of them we do not have a suitable tag.
My question is how should the situation be resolved:
- Should we use products for more abstract meaning of the word product, too? (In this case maybe product-space could be made synonym of this tag.)
- Should we use products only for the posts about product as a binary operation? If we decide on this usage, should we create a separate tag (or even several tags) for products of various mathematical structures?
EDIT: It seems that the infinite-product tag has the same issues. There are some questions tagged infinite-product+general-topology, infinite-product+group-theory, infinite-product+category-theory. They seem to be about the product in the abstract sense rather than about product of sequence of numbers.
(I am not sure whether the two tags are different enough so that we need a separate thread about infinite-product. But if somebody feels that it would be better to discuss them separately and posts a new question, I will remove the above paragraph and just add a link to other thread instead.)