Pointfree Functorial Polar Functions
Applied Categorical Structures
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.
Carrera, Ricardo Enrique, "Pointfree Functorial Polar Functions" (2016). Mathematics Faculty Articles. 95.