The question is to show that an additive functor $F$ between two categories Of left $R$-modules will send the $0$-module to the $0$-module.
How to prove this?
2026-04-12 17:51:15.1776016275
An additive functor between two categories of left $R$-modules sends zero module to zero module.
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Additive functors preserves zero objects. In the category of modules, zero modules are both initial and terminal, hence are preserved by additive functors.