Injectivity is a property of functions that indicates a one-to-one correspondence between elements of the domain and the codomain, meaning that different elements in the domain map to different elements in the codomain. This concept plays a crucial role in various mathematical contexts, particularly in determining whether morphisms in categories preserve structure and enable certain constructions. In homological algebra, understanding injectivity is vital for applying the snake lemma, as it helps clarify how certain sequences can be analyzed and manipulated.
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