Sentence:  If \mathbf{A} is the category of sets, then \Pi_B f is (up to isomorphism) the usual Cartesian product of the fibres A_y. If \mathbf{A} is a category of spaces and smooth maps, then an element of \Pi_B f will have values varying smoothly in the indices, while if \mathbf{A} models data types and computable functions the values will vary <WSD>computably</WSD>. 
Meaning of the word marked with <WSD> tags:  In a computable manner