We give an overview of five rationalization theories for spaces (Bousfield-Kan's ℚ-
completion; Sullivan's rationalization; Bousfield's homology rationalization; Casacuberta …

We give a short and streamlined proof of the following statement recently proven by the
author and M. Zeinalian: the cobar construction of the dg coassociative coalgebra of …

Bousfield and Kan's ℚ–completion and fiberwise ℚ–completion of spaces lead to two
different approaches to the rational homotopy theory of nonsimply connected spaces. In the …

We use derived localization of the bar and nerve constructions to provide simple proofs of a
number of results in algebraic topology, both known and new. This includes a recent …

We prove that the simplicial cocommutative coalgebra of singular chains on a connected
topological space determines the homotopy type rationally and one prime at a time, without …

We show that the notions of homotopy epimorphism and homological epimorphism in the
category of differential graded algebras are equivalent. As an application we obtain a …

We show that the notions of homotopy epimorphism and homological epimorphism in the
category of differential graded algebras are equivalent. As an application we obtain a …

One of the questions that gave birth to rational homotopy theory is the commutative cochains
problem, which, given a commutative ring k, asks whether there exists a commutative …