Why are chains topologically analoguous to distributions?

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This question is related to my other question here but is different enough that I thought I might ask separately.

At the nLab page on rational homotopy theory it is stated that chains are topologically analoguous to distributions.

Could someone explain this analogy to me? In particular I would like to understand why this implies that the enveloping algebra of a Lie algebra could be thought of as the algebra of distributions supported at the identity.

Perhaps a reference to a good place to read about these kinds of subjects?