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Let $ S,T$ be abstract simplicial complexes. Is there a (unique) abstract simplicial complex that gives me the most of what is in common with $ S$ and $ T$ ? I’m thinking of this as an “intersection,” or “refinement” of the two complexes, maybe a “core” that has the most properties of both. IRead more

Assume given a pullback square of simplicial categories $ $ \begin{array}[c]{ccc} A&{\rightarrow}&B\ \downarrow&&\downarrow\ C&{\rightarrow}&D. \end{array}$ $ Suppose further that one of the induced arrows $ Ho (B) \to Ho(D)$ or $ Ho(C) \to Ho(D)$ is an isofibration, and for each couple of objects $ x,y \in A$ , the induced pullback square of simplicial mappingRead more

Let $ K$ be a simplicial complex: it consists from the set (called the set of vertices) and a family of subsets of set of vertices satisfying the property of being closed under taking subsets (those set are called simplices: condition translates that the subset of a simplex is again simplex). Homology of simplicial complexRead more