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An obstruction theory for simplicial categories. (English) Zbl 0609.55009
Let SO-Cat be the category of category objects in the category S of simplicial sets, having a fixed set O of objects. The morphisms in SO-Cat are simplicial, object preserving functors. The authors develop an obstruction theory for inserting the dotted arrow into a commutative solid arrow diagram in SO-Cat in which \(A\to B\) is a cofibration and \(X\to Y\) a fibration.