On a common generalization of funcoids and reloids

Just a few seconds ago I had an idea how to generalize both funcoids and reloids.

Consider

  • a precategory, whose objects are sets
  • product \times of filters on sets ranging in morphisms of this category
  • operations \mathrm{dom} and \mathrm{im} from the morphisms of our precategory to filters on our objects (sets)

This axiomatic system is so powerful that it allows to define \langle f\rangle for a funcoid f:

\langle f\rangle\mathcal{X} = \mathrm{im}(f\circ(1^\mathfrak{F}\times^\mathsf{FCD}\mathcal{X})).

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