I would like some clarification on the idea of a $\Delta$-complex:
It seems that we can identify edges of a triangulated polygon to obtain $2$-dimensional spaces and the idea of a $\Delta$-complex is to break any object up into simplices of various dimensions identifying $n$-cells. A $\Delta$-complex then is a collection $\{\Delta_0,\Delta_1,\Delta_2,\cdots,\Delta_n\}$ where identify basis elements of these $\Delta_i$ with other elements within the same $\Delta_i$. Where the basis elements are the $i$-cells of the complex?
Could someone check this for misunderstandings? I am mainly worried about how the latter seems to feel pinned on only being relevant to a single $n$-simplex, whereas I feel the $i$-cells shouldn't be identified away from a single $n$-simplex, where more than one may exist in the $\Delta$-complex (right?)