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To my understanding, isospin was introduced for nucleons (neutrons and protons) because of their similar properties. When it was found out that they are made up of quarks, naturally the quarks could also be assigned isospin.

Is it then from the quark isospins that we can assign isospin to all hadrons?

Would it be more correct to say that isospin comes from quarks rather than nucleons (for which it was inteoduced)?

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    $\begingroup$ you can say the same for baryon number too, and charge $\endgroup$ – anna v May 19 '17 at 17:19
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Isospin symmetry is a subset of the flavour symmetry seen more broadly in the interactions of baryons and mesons. Isospin symmetry remains an important concept in particle physics. A close examination of this symmetry, historically, led directly to the discovery and understanding of quarks and of the development of Yang–Mills theory.

As modeling developed into the quark model, with the table of quarks as seen in the standard model of physics, the isospin became the quantum number characterizing the quarks as seen in protons and neutrons, to separate the strangeness and charm couple (generation) , and the top and bottom couple. Analogously one might say "upness" and "downness". The algebra is the SU(2) group algebra when building up the isospin of hadrons.

Up and down quarks each have isospin I =  1⁄2, and isospin 3-components (I3) of  1⁄2 and − 1⁄2 respectively. All other quarks have I = 0. In general

ispin

Would it be more correct to say that isospin comes from quarks rather than nucleons

Yes, keeping in mind that in particular it defines up and down quarks only.

In particle physics it is not a very useful concept, other than in separating up from down quarks. (The rest of the quarks have individual names instead of a spin type representation). This answer of mine to a different questions is related

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