isotopy equivalence of maps

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In the book Encyclopaedia of Mathematics, Vol. 6,

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Question: I do not understand the part enter image description here

Does this mean $F_1\circ f_0=f_1: X\to Y$ or as subsets of $Y$, $$ \{y\in F_1(f_0(X))\}=\{y\in f_1(X)\}? $$