Homomorphism of algebraic groups

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Definition

Concrete definition

Suppose G_1 and G_2 are algebraic groups over a field k. A 'homomorphism of algebraic groups is a function \varphi:G_1 \to G_2 satisfying both these conditions:

  1. \varphi is a homomorphism of groups.
  2. \varphi is a morphism of algebraic varieties.