nLab dyadic interval coalgebra




A dyadic interval coalgebra is a set II with a linear order <\lt, elements 0I0 \in I and 1I1 \in I and functions z 0:IIz_0:I \to I and z 1:IIz_1:I \to I, such that z 0(0)=0z_0(0) = 0, z 1(0)=0z_1(0) = 0, z 0(1)=1z_0(1) = 1, z 1(1)=1z_1(1) = 1, * for all elements aIa \in I, 0<a0 \lt a or a<1a \lt 1, and for all elements aIa \in I, it is false that both 0<z 0(a)0 \lt z_0(a) and z 1(a)<1z_1(a) \lt 1.

This is called simply an interval coalgebra by Peter Freyd, however there exist similarly defined interval coalgebras with n+1n+1 terms and nn zooming operations, such as the decimal interval coalgebra.


See also


  • Peter Freyd, Algebraic real analysis, Theory and Applications of Categories, Vol. 20, 2008, No. 10, pp 215-306 (tac:20-10)

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