Abstract
We introduce weak topological functors and show that they lift and preserve weak limits and weak colimits. We also show that if A ! B is a topological functor and J is a category, then the induced functor AJ ! BJ is topological. These results are applied to a generalization of Wyler’s top categories and in particular to functor categories of fuzzy maps, fuzzy relations, fuzzy topological spaces and fuzzy measurable spaces.
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