# Representable presheaves of groups on the homotopy category of cocommutative dg-coalgebras and Tannakian reconstruction

Research paper by Jaehyeok Lee, Jae-Suk Park

Indexed on: 14 May '19Published on: 21 Mar '19Published in: arXiv - Mathematics - Algebraic Geometry

#### Abstract

Motivated by rational homotopy theory, we study a representable presheaf of groups $\mathbf{\mathfrak{P}}$ on the homotopy category of cocommutative differential graded coalgebras, its Lie algebraic counterpart and its linear representations. We prove a Tannaka type reconstruction theorem that $\mathbf{\mathfrak{P}}$ can be recovered from the dg-category of its linear representations along with the forgetful dg-functor to the underlying dg-category of chain complexes.