Tail recursion from universal invariants
The categorical account of lists is usually given in terms of initial algebras, i.e. head recursion. But it is also possible to define them by interpreting tail recursion by means of the colimit of a loop diagram, i.e. its universal invariant. Parametrised initial algebras always have universal invariants, while the converse holds in the presence of equalisers.
Consequences include categorical descriptions of vectors and matrices, which allow definitions of inner products, transposes and matrix multiplication.
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