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Sum Types

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Bool
Introduction, elimination and computation rules
Data constructors as functions (morphisms), in this case from the terminal object (since they are nullary).
Enumerations
Big enumerations
Case statement as an enumeration elimination pattern
Pattern matching as an enumeration elimination rule
Nullary data constructors as the enumeration introduction rule
Either
Functions (computation rules) from Either
Maybe
Functoriality/lifting for sum types