functor composition

1. Definition / Proposition

Let 20230301211128-komposition_von_funktoren_7bea27db726988eb947effe3356a711538031817.svg be categories and 20230301211128-komposition_von_funktoren_b54ab6ad05f4c4521b8f1b2dbd89918fb6a3ea70.svg and 20230301211128-komposition_von_funktoren_cf345396c41fb0d12732c4e02c2d9bc343100c7c.svg be functors. Then the composition 20230301211128-komposition_von_funktoren_3ce2bc4e6b8e9fa8174a7b318d257ea8389b9c5a.svg defined by:

20230301211128-komposition_von_funktoren_8fa0b3b1e34fdd3a7bd7d72d50337ebdc4d94673.svg

for 20230301211128-komposition_von_funktoren_fa924026bd3ec7075e3f483dfe52555d0035adbb.svg and 20230301211128-komposition_von_funktoren_c94aa42108966737b1d59b132f48539636c46e08.svg is also a functor 20230301211128-komposition_von_funktoren_7406a13acd5cb28e19d5b135f4187d373cbecf95.svg

2. Proof

follows from the commutativity of the following diagram

20230301211128-komposition_von_funktoren_4a0c7cb8d06f3c111bda2807169c91b07dfdf9b0.svg

Date: nil

Author: Anton Zakrewski

Created: 2024-10-11 Fr 22:06