Domain of discourse


I also use the following types to classify the bulk of other entries in the wiki and these are the entries with formal content.

  • ${\mathfrak D}_\mathrm{Sets}$ … Sets
  • ${\mathfrak D}_{\to}$ … Functions
  • ${\mathfrak D}_\mathrm{Cats}$ … Categories
  • ${\mathfrak D}_{\longrightarrow}$ … Functors
  • ${\mathfrak D}_{\xrightarrow{\bullet}}$ … Natural transformations
  • ${\mathfrak D}_\mathrm{Tuples}$ … Tuples, finite lists of elements of the above sorts
  • ${\mathfrak D}_\mathrm{Collections}$ … Collections, ad hoc subclasses of the above sorts (I use this as in some sort of naive set theory)

The domains themselves are primitive notions. Usage and axiomatics of those domains are discussed in entries of type Framework.

All Set entry definitions are purposely free from terms of the other domains, except for functions and tuples of sets (though tuples and also the functions we consider can just as well be modeled within a set theory, so that's just for clarity.). In this way, the set entries in this wiki can e.g. be interpreted as defining object within formal ZFC.

There are also entries of type Type. The discussion of type theories in this wiki does not overlap with the above notions.


todo: summarize how some of them can be thought of a special cases of others

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