Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
397712 | International Journal of Approximate Reasoning | 2013 | 18 Pages |
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.
► An adjunction is presented between categories of closure spaces and complete lattices. ► An adjunction is presented between categories of formal contexts and closure spaces. ► A decomposition is obtained for the formal concept lattice functor.