We discuss three different types of (weakly) convex geodesic bicombings on metric spaces and clarify the relations between them. Every injective metric space (or absolute 1-Lipschitz retract) admits a bicombing of the weakest type. We prove an existence and uniqueness result for bicombings of the strongest type. This is related to our ongoing investigation of injective hulls of discrete metric spaces and hyperbolic groups.
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