  Formal concept analysis (FCA) is built on a special type of Galois
connections called polarities. We present new results in formal concept
analysis and in Galois connections by presenting new Galois connection results
and then applying these to formal concept analysis. We also approach FCA from
the perspective of collections of formal contexts. Usually, when doing FCA, a
formal context is fixed. We are interested in comparing formal contexts and
asking what criteria should be used when determining when one formal context is
better than another formal context. Interestingly, we address this issue by
studying sets of polarities.
