# Topologies and Sheaves

@inproceedings{Tamme1994TopologiesAS,
title={Topologies and Sheaves},
author={G{\"u}ter Tamme},
year={1994}
}
Let X be a topological space, and let T denote the family of all open subsets of X. T becomes a category if we define $$Hom(U,V) = \left\{ {\begin{array}{*{20}{c}} 0&{if U \not\subset V} \\ {inclusion U \to V}&{if U \subset V} \end{array}} \right.$$ for U,V ∈ T. X is a final object in the category T. The intersection ∩U i of finitely many U1,…, U n in T is equal to the product of the U1,…, U n in the category T. The union ∪ U i of arbitrarily many U i in T is equal to the direct sum of… CONTINUE READING