morphism of pair of ideals induces morphism on pullbacks

Proposition

Let 20241026-morphism_of_pair_of_ideals_induces_morphism_on_pullbacks_2a56cd9dfa497436a8464642f38715d62b544d7c.svg be a ring-homomorphism, 20241026-morphism_of_pair_of_ideals_induces_morphism_on_pullbacks_142b66778c73c54a23621cb1c1db74d535d0b300.svg ideals such that 20241026-morphism_of_pair_of_ideals_induces_morphism_on_pullbacks_8fd4e595116b47b81cc5a3a14de3b56fe7469c31.svg.
Then there exists a canonical induced morphism

20241026-morphism_of_pair_of_ideals_induces_morphism_on_pullbacks_01ad66bd5becf1e1d85fe7711b7dbdccf1b546c5.svg

Proof

follows from lim functor and the evident natural transformation

20241026-morphism_of_pair_of_ideals_induces_morphism_on_pullbacks_73cac1751ceb4e307dad1fe76e7daddb79b15f34.svg

Date: nil

Author: Anton Zakrewski

Created: 2025-01-15 Mi 18:17