Topological Functors via Closure Operators

Abstract

In this article for a given category X , we fully embed certain categories of closure operators on a given collection M ⊆ X1, in certain categories of preclass-valued lax presheaves on X . We then fully embed the just mentioned categories of preclass-valued lax presheaves on X , in certain categories of topological functors on X . Combining the full embeddings obtained, we construct a topological functor from a given closure operator.

Keywords

• Closure operator,lax presheaf,lax natural transformation,(complete) preordered or partially ordered class,(weak) topological functor

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