precisely, in the theory of simplicial sets, the Dold–Kan correspondence (named after Albrecht Dold and Daniel Kan) states that there is an equivalence between...

with a structure of an algebra. In view of the module-variant of Dold–Kan correspondence, the notion of an N 0 {\displaystyle \mathbb {N} _{0}} -graded...

simplicial localizations of relative categories. Dold–Kan correspondence Kan extension Daniel Kan at the nLab Kan, Daniel M. (1958). "Adjoint functors". Transactions...

groups. A simplicial group is a Kan complex (in particular, its homotopy groups make sense). The Dold–Kan correspondence says that a simplicial abelian...

weak Kan condition. Delta set Dendroidal set, a generalization of simplicial set Simplicial presheaf Quasi-category Kan complex Dold–Kan correspondence Simplicial...

complex Differential graded algebra Differential graded Lie algebra Dold–Kan correspondence says there is an equivalence between the category of chain complexes...

Dold (5 August 1928 – 26 September 2011) was a German mathematician specializing in algebraic topology who proved the Dold–Thom theorem, the Dold–Kan...

it is a simplicial abelian group, and thus is subject to the Dold–Kan correspondence. Differential graded Lie algebra Quillen, Daniel (September 1969)...

correspond to Kan complexes of some simplicial set. In fact, this set can be constructed explicitly using the Dold–Kan correspondence of a chain complex...

{\displaystyle \pi _{p+q}\operatorname {colim} X(i).} By the Dold–Kan correspondence, this generalizes the construction of the spectral sequence associated...