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A Kleisli-based approach to lax algebras

Gavin J. Seal
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Abstract

By exploiting the description of topological spaces by either neighborhood systems or filter convergence, we obtain a neighborhood-like presentation of categories of lax algebras. A notable advantage of this approach is that it does not require the introduction of a lax extension of the associated monad functor. As a byproduct, the different philosophies underlying the construction of fuzzy topological spaces on one hand, and approach spaces on the other, may be simply expressed in terms of lax algebras.

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Gavin J. Seal. 2006-08-08. A Kleisli-based approach to lax algebras. https://arxiv.org/abs/math/0510281

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