# A general theory of self-similarity

@article{Leinster2010AGT, title={A general theory of self-similarity}, author={Tom Leinster}, journal={arXiv: Category Theory}, year={2010} }

A little-known and highly economical characterization of the real interval [0, 1], essentially due to Freyd, states that the interval is homeomorphic to two copies of itself glued end to end, and, in a precise sense, is universal as such. Other familiar spaces have similar universal properties; for example, the topological simplices Delta^n may be defined as the universal family of spaces admitting barycentric subdivision. We develop a general theory of such universal characterizations.
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