# What is the universal property of the tangent bundle of a smooth manifold?

The process of writing my own notes on smooth manifolds have led me to wonder about this. All I've really found is the following:

In addition to Madame Ehresmann's references, there is in Spivak's Comprehensive Introduction... an abstract characterization of the tangent bundle ( removed from the main text in the second edition `due to the pressure of public distaste')

I have neither Madame Ehresmann's notes, nor an older edition of Spivak.

Sincerely, Eivind

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