multiplication alignment table

If only I knew what a tensor product was

Took me a while to find out what I think these all are, still not 100% on some of them. From top left, going right:

• Multiplication over the rationals
• Wedge product / alternating product
• Function composition (ring operator)
• Inner product (e.g. scalar product)
• Tensor product
• Lie bracket
• Set intersection
• Vector product / cross product
• Tor functor

Corrections welcome!

what is the thing at the top of the middle column