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Is it reductionist to say "Universal properties are the central concept of Category Theory". And if so, is it a useful fiction to keep in ones head as they are learning the subject?

Polymer
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  • See https://math.stackexchange.com/a/63160/589 – lhf Nov 13 '18 at 22:31
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    The nice thing about category theory is that it admits several central concepts, each of which can be reduced to the others: universal properties, adjoint functors, Kan extensions, etc. – Qiaochu Yuan Nov 13 '18 at 22:43
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    Those definitions are all "equivalent"? – Polymer Nov 13 '18 at 23:26
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    They're not equivalent, but they're interdefinable. Limits and colimits are special cases of Kan extensions, which are a special case of initial and terminal objects, which are a special case of adjoint functors, which are a type of Kan extension... – Malice Vidrine Nov 14 '18 at 00:43
  • Okay, thank you. – Polymer Nov 14 '18 at 00:59

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