symmetric monoidal (∞,1)-category of spectra
The idea of a midpoint algebra comes from Peter Freyd.
A midpoint algebra is a magma that is commutative, idempotent, and medial:
for all in ,
for all and in ,
for all , , , and in ,
The currying of the midpoint operation results in the contraction . Contractions are midpoint homomorphisms: for all , , and in , .
The rational numbers, real numbers, and the complex numbers with are examples of midpoint algebras.
The trivial group with is a midpoint algebra.
Peter Freyd, Algebraic real analysis, Theory and Applications of Categories, Vol. 20, 2008, No. 10, pp 215-306 (tac:20-10)
Martín Escardó and Alex Simpson. A universal characterization of the closed Euclidean interval. In 16th Annual IEEE Symposium on Logic in Computer Science, Boston, Massachusetts, USA, June 16-19, 2001, Proceedings, pages 115–125. IEEE Computer Society, 2001. (doi:10.1109/LICS.2001.932488, pdf)
Last revised on December 26, 2023 at 06:55:11. See the history of this page for a list of all contributions to it.