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We define what we call morphisms of Cartan connections. We generalize themain theorems on Cartan connections to theorems on morphisms. Many of the knownconstructions involving Cartan connections turn out to be examples ofmorphisms. We prove some basic results concerning completeness of Cartanconnections. We provide a new method to prove completeness of Cartanconnections using families of morphisms.

Morphisms of Cartan connections