tail equivalence in the category of series

Consider the category Series.

Say that two objects of Series are tail-equivalent if and only if their quotient with respect to their variables (as the index is increased without bound) is one.

For instance \sum_{n=1}^{\infty} q^{n^{2}} and  \sum_{n=1}^{\infty} q^{n^{2}-q^{n}} 

We’ll write \sum_{n=1}^{\infty} q^{n^{2}} \sim \sum_{n=1}^{\infty} q^{n^{2}-q^{n}}

I believe \sim is an equivalence relation. But lo, what of the quotient category Series/\sim


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s