Pulling a continuous map back along an embedding

Stream: general

[Brendan Seamas Murphy]

If I have f : C(X, Y) and i : C(A, Y) and I know embedding i and set.range ⇑f ⊆ set.range ⇑i, how can I get a g : C(X, A) such that ⇑f = ⇑i ∘ ⇑g?

[Brendan Seamas Murphy]

...oh, it looks like I already ran into this while working on this project and just defined it myself