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?
Asked
Active
Viewed 62 times
1
-
See https://math.stackexchange.com/a/63160/589 – lhf Nov 13 '18 at 22:31
-
5The 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
-
1Those definitions are all "equivalent"? – Polymer Nov 13 '18 at 23:26
-
3They'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