4 problems

Let $X$ and $Y$ be homotopy types, and associate to each its simplicial cocommutative $\mathbb{F}$-coalgebra of chains, regarded up to $\widehat{\mathbb{\Omega}}$-quasi-isomorphism…

Let $X$ and $Y$ be reduced Kan complexes. Write $4\mathbb{Z}X4$ and $4\mathbb{Z}Y4$ for their connected simplicial cocommutative coalgebras of integral chains. Two such coalgebras…

Let $X$ be a connected space, and consider its simplicial cocommutative coalgebra of integral singular chains. Integral detection conjecture without finite-type assumptions. The in…

Let $X$ be a connected topological space, and let its singular chains with integral coefficients be regarded as a simplicial coalgebra via the diagonal. Integral detection conjectu…