Abstract
The Cartan formula encodes the relationship between the cup product and the action of the Steenrod algebra in Fp-cohomology. In this work, we present an effective proof of the Cartan formula at the cochain level when the field is F2. More explicitly, for an arbitrary pair of cocycles and any non-negative integer, we construct a natural coboundary that descends to the associated instance of the Cartan formula. Our construction of Cartan coboundaries works for general algebras over the Barratt-Eccles operad, in particular, for the singular cochains of spaces, a case for which we have developed open source software.
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