论文信息 - A Kleisli-based Approach to Lax Algebras

A Kleisli-based Approach to Lax Algebras

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. The simplicity of this presentation pinpoints the importance of the Kleisli extension, which is introduced as a particular lax extension of the associated monad functor.

Gavin J. Seal

[1] Gavin J. Seal. CANONICAL AND OP-CANONICAL LAX ALGEBRAS , 2005 .

[2] Werner Gähler,et al. The general fuzzy filter approach to fuzzy topology, II , 1995, Fuzzy Sets Syst..

[3] Jirí Adámek,et al. Abstract and Concrete Categories - The Joy of Cats , 1990 .

[4] Claudio Pisani,et al. CONVERGENCE IN EXPONENTIABLE SPACES , 2001 .

[5] Dirk Hofmann,et al. KLEISLI OPERATIONS FOR TOPOLOGICAL SPACES , 2004 .

[6] Dexue Zhang. Tower extension of topological constructs , 2000 .

[7] R. Lowen. Approach Spaces: The Missing Link in the Topology-Uniformity-Metric Triad , 1997 .

[8] Dirk Hofmann,et al. On extensions of lax monads , 2004 .

[9] Dirk Hofmann,et al. Kleisli compositions for topological spaces , 2006 .

[10] U. Höhle. Many Valued Topology and its Applications , 2001 .

[11] Raster convergence with respect to a closure operator , 2005 .

[12] R. J. Wood. Ordered Sets via Adjunctions , 2002 .

[13] Walter Tholen,et al. Metric, topology and multicategory—a common approach , 2003 .

[14] Paul Brock,et al. Approach Spaces, Limit Tower Spaces, and Probabilistic Convergence Spaces , 1997, Appl. Categorical Struct..

[15] Dirk Hofmann,et al. One Setting for All: Metric, Topology, Uniformity, Approach Structure , 2004, Appl. Categorical Struct..

[16] C. Schubert. Lax Algebras: A Scenic Approach , 2006 .