Does the Curl of a Force Vector Change Its Dimensionality?

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Suppose we begin with F which is a force..

Does taking the curl of a force such as

\nabla \times F

state that this expression no longer has dimensions of force? What I mean is, does the nabla operator have dimensions, and so would this change the dimensions of the expression?
 
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1) You can only take the curl of a vector field, not of a single vector.

2) The curl is basically a spatial derivative and so will bring down a 1/length unit. The curl of a force field is then in units of force/length.
 
Thank you.
 
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