Tootfinder

Comparing dg category models for path spaces via $A_\infty$-functors
Manuel Rivera, Yi Wang
https://arxiv.org/abs/2510.01080 https://arxiv.org/pdf/2510.010…

Comparing dg category models for path spaces via $A_\infty$-functors
We construct a many-object dual version of Chen's iterated integral map. For any topological space X, the construction takes the form of an A-infinity functor between two dg categories whose objects are the points of X: the domain has as morphisms the singular (cubical) chains on the space of (Moore) paths in X and the codomain has morphisms arising by totalizing a cosimplicial chain complex determined by the dg coalgebra of singular (simplicial) chains in X. When X is simply connected, we show…