nLab free graded co-commutative coalgebra


For V V^\bullet a complex of modules over a commutative algebra AA, the free graded co-commutative coalgebra A V\vee^\bullet_A V over VV, is the coalgebra (in the sense of co-monoids in complexes of modules) whose underlying complex is the graded-symmetric tensor algebra S A VS^\bullet_A V over AA, and who co-product is the co-concatenation product.

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