Superscript L in tensor product

Question

I was reading this short note: https://arxiv.org/abs/2008.03155. On the top of page 2, there’s the expression $M\otimes_A^LN$. The subscript of course is just saying which ring we’re taking the tensor product over, but I can’t figure out what this $L$ is supposed to mean. Any help would be appreciated!

Answer 1

It stands for the derived tensor product in the derived category of $A$. This is a special case of a left-derived functor, whence the $L$.