Abstract. This paper studies various functors between (latticevalued) topology and (lattice-valued) bitopology, including the ex-2 -Top introduced in this paper, both of which are extremely well-behaved strict, concrete, full embeddings. Given the greater simplicity of lattice-valued topology vis-a-vis latticevalued bitopology and the fact that the class of L 2 -Top's is strictly smaller than the class of L-Top's encompassing fixed-basis topology, the class of E×'s makes the case that lattice-valued bitopology is categorically redundant. As a special application, traditional bitopology as represented by BiTop is (isomorphic in an extremely well-behaved way to) a strict subcategory of 4-Top, where 4 is the four element Boolean algebra; this makes the case that traditional bitopology is a special case of a much simpler fixed-basis topology.

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