I've never really thought much about distributivity of limits and colimits -- I tend to think more about commutativity of limits and colimits. This question makes me want to change that.

The question of which limits commute with which colimits in the category of sets has a complicated answer, but important special cases which are not so complicated. This leads to the title question:

Question: Which limits distribute over which colimits in $Set$?

Is it complicated like with commutativity? Or is it maybe simpler? If it's complicated, are there good simplifying assumptions one can make?

I've never really thought much about distributivity of limits and colimits -- I tend to think more about commutativity of limits and colimits. This question makes me want to change that.

The question of which limits commute with which colimits in the category of sets has a complicated answer, but important special cases which are not so complicated. This leads to the title question:

Question:

1. Which limits distribute over which colimits in the 1-category $Set$?

2. Which limits distribute over which colimits in the $\infty$-category $Spaces$?

Is it complicated like with commutativity? Or is it maybe simpler? If it's complicated, are there good simplifying assumptions one can make?