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I think of static friction as a "responding" force. For
example, a crate pulled to the right (by a rope) will
experience a responding force (from the floor) directed
to the left.
That way of thinking anthropomorphises the force,
which is usually irrelevant and sometimes misleading.
F does not "cause" ma, and ma does not "cause" F,
for reasons discussed at
http://www.av8n.com/physics/causation.htm