That is expected because 2-connected is a stronger property than

1-connected.

This correspondence yields an equivalence between the homotopy categories of rational

1-connected CW-complexes of finite type and

1-connected cdga's of finite type.

A

1-connected complex is usually called simply connected: any loop (closed path) can be continuously deformed to a point.

Throughout this section B denotes a 1-connected CW-complex with H*(B) = H*(B; Z/(p)) = Z/(p)[[x.

Let f : X [approaches] B and g : Y [approaches] B be CW-complexes over B (B-CW-complexes for short) with Y 1-connected.

However, this is not a J-category and the Eckmann-Hilton dual of a partial version of the cube axiom is satisfied when restricting to 1-connected algebras [6, A.

of cofibrant 1-connected commutative differential graded algebras of finite type over Q (known as Sullivan algebras [11, [section]12]) and 1-connected rational Kan complexes of finite type, then they do preserve weak equivalences and via [6, Prop.

8], Fasso introduced, for a map of finite type 1-connected CW-complexes, or equivalently for a simplicial map of finite type 1-connected Kan complexes E [?

Every node can be in one of the following three states: 0-connected, 1-connected and 2-connected.

con=2) 18 construct an ear using u and v's upstream paths; 19 for each 1-connected node e in the ear 20 D[e].

4 (c), two 1-connected trees {1,3,4,7,8} and {2,5,6} meet at node 9 and a normal ear {1,3,8,9,5,2} is found and augmented.

It is easy to see that X is

1-connected and locally

1-connected.