Is there a well known product structure for Frames? I.e. if $L$ and $L^{\prime}$ are frames, is there a product object in $\mathbf{Frm}$ category isomorphic to an object with underlying set the set product $L\times L^{\prime}$, and what is its order?
Also, I think this will be answered when the former is but just in case it won't, Is the case for coframes substantially different?
I wrote the question before trying to answer it because thought it would be harder or an obscure definition.
Anyway, the usual product order works over the usual set product:
$(x_{1},y_{1})\leq (x_{2},y_{2})$ iff $x_{1}\leq x_{2}$ and $y_{1}\leq y_{2}$.