Coalgebraic Approach to the Loday Infinity Category, Stem Differential for -ary Graded and Homotopy Algebras
We define a graded twisted-coassociative coproduct on the tensor algebra the desuspension space of a graded vector space . The coderivations (resp. quadratic “degree 1” codifferentials, arbitrary odd codifferentials) of this coalgebra are 1-to-1 with sequences of multilinear maps on (resp. graded Loday structures on , sequences that we call Loday infinity structures on ). We prove a minimal model theorem for Loday infinity algebras and observe that the category contains the category as...