natural transformation

1. Definition

Let 20220821182915-naturliche_transformation_kategorientheorie_2d5d1c2bfbb1a2fca757f722875cd0787290c048.svg be categories and 20220821182915-naturliche_transformation_kategorientheorie_57a6502a6c9b34b1556972b503a619b5ee3b2b0b.svg a (covariant, resp. contravariant) functor.

Then a natural transformation 20220821182915-naturliche_transformation_kategorientheorie_aa699af8b052820cdd98bf8bee54004084151ed7.svg assigns to each object 20220821182915-naturliche_transformation_kategorientheorie_fa924026bd3ec7075e3f483dfe52555d0035adbb.svg a

20220821182915-naturliche_transformation_kategorientheorie_863595cb3461bcca03b8d0ba73fb8d358e1f6473.svg

such that for each 20220821182915-naturliche_transformation_kategorientheorie_6ffd8ea1a86d28129d6e92f5d3f95dda5ef98432.svg following diagram commutes

20220821182915-naturliche_transformation_kategorientheorie_0ece3e6cabc3844a258c91c81d8b11c82789fa9c.svg

Note that a natural transformation between contravariant functors is given by

20220821182915-naturliche_transformation_kategorientheorie_aca433750c4d41eea3ed8f4d9d20f5ee62815129.svg

Date: nil

Author: Anton Zakrewski

Created: 2024-10-11 Fr 21:30