That's a good point. Maybe the word "adulteration" or "bastardization" would be better? Or maybe to avoid odd connotations I should just say it in long form: taking a mathematical machete to a product space and making it nearly unrecognizable.
I do still think, despite what many have said, that a comparison and distinction needs to be made between usual products and tensor products. I think "modifying a product space" happens to be a different way of thinking about it (maybe not the best way), and for what it's worth it helps me keep track of the damn things.
I do still think, despite what many have said, that a comparison and distinction needs to be made between usual products and tensor products. I think "modifying a product space" happens to be a different way of thinking about it (maybe not the best way), and for what it's worth it helps me keep track of the damn things.