association type for model hasMany or HABTM

does my observation and solution seem correct in my association below?

1) i have a products table and a categories table

2) each product has a category associated with it

3) and each category has products associated with it

So there could be many products in one category, and many categories with one product.

My assumption is I will need to use an HABTM association.

Am I evaluating this properly? Or would HABTM be overkill for my purposes?
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