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Let Top and Diff be the categories of topological and diffeological spaces, respectively. By using an adjunction between Top and Diff we show that the full subcategory NG of Top consisting of numerica...lly generated spaces is complete, cocomplete and cartesian closed. In fact, NG can be embedded into Diff as a cartesian closed full subcategory. It follows then that the category NG_0 of numerically generated pointed spaces is complete, cocomplete and monoidally closed with respect to the smash product. These features of NG_0 are used to establish a simple but flexible method for constructing generalized homology and cohomology theories by using the notion of enriched bifunctors.続きを見る
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