The concept lattice functors

  • Authors:

  • Lili Shen;Dexue Zhang

  • Affiliations:

  • School of Mathematics, Sichuan University, Chengdu 610064, China;School of Mathematics, Sichuan University, Chengdu 610064, China

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2013

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Abstract

This paper is concerned with the relationship between contexts, closure spaces, and complete lattices. It is shown that, for a unital quantale L, both formal concept lattices and property oriented concept lattices are functorial from the category L-Ctx of L-contexts and infomorphisms to the category L-Sup of complete L-lattices and suprema-preserving maps. Moreover, the formal concept lattice functor can be written as the composition of a right adjoint functor from L-Ctx to the category L-Cls of L-closure spaces and continuous functions and a left adjoint functor from L-Cls to L-Sup.