exact sequence
[ɪɡˈzækt ˈsiːkwəns]
nounpl: exact sequences
sequência exata
1. In mathematics, particularly in homological algebra, a sequence of objects and morphisms where the image of one morphism equals the kernel of the next
The long exact sequence in homology is a fundamental tool in algebraic topology.
A sequência exata longa em homologia é uma ferramenta fundamental em topologia algébrica.
2. A chain complex where every three consecutive terms satisfy the condition that composition of consecutive maps equals zero and the image of each map equals the kernel of the next
We need to verify that this is an exact sequence before applying the Snake Lemma.
Precisamos verificar que se trata de uma sequência exata antes de aplicar o Lema da Serpente.
This is specialized mathematical terminology used uniformly across English and Portuguese-speaking academic and research communities. The concept originated in mid-20th century homological algebra and is essential in advanced mathematics coursework. There are no colloquial or regional variations in meaning; the term maintains strict technical definition regardless of geographic region.
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