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Pointfree Functorial Polar Functions
Applied Categorical Structures
  • Ricardo Enrique Carrera, Nova Southeastern University
Document Type
Publication Date
  • Pointfree polar functions,
  • Functorial polar functions,
  • Hull class,
  • Skeletal maps,
  • Compact regular frame,
  • α-disconnected frame,
  • α-cloz frame
C denotes the category of compact regular frames with frame homomorphisms. A function XX , which assigns to each C-object F a subalgebra of P(F)P(F) that contains the complemented elements of F is said to be a polar function. An essential extension H of F is a XX -splitting frame of F if whenever p∈X(F)p∈X(F) , then the polar generated by p in H is complemented. For F∈ C we examine the least XX -splitting extension and prove that every invariant polar function generates a C-hull class of frames. In addition, we define the concept of a functorial polar function and prove that each functorial polar function generates an epireflective subcategory of the category compact regular frames with skeletal maps.
Citation Information
Ricardo Enrique Carrera. "Pointfree Functorial Polar Functions" Applied Categorical Structures Vol. 24 Iss. 1 (2016) p. 37 - 52 ISSN: 0927-2852
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