Propositions as Types generalised: The Rosetta Stone

From Physics,Topology, Logic and Computation: A Rosetta Stone by John C. Baez and Mike Stay, courtesy of @CompSciFact, @sigfpe, and @notjfmc.

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In which way is a cobordism a function between manifolds? As far as I know a cobordism is itself a manifold.
A cobordism is a continuous transformation of one border into another (hence a function). Because it is continuous, it may also be considered as a manifold.
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