# Exactness

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**Splitting lemma**— In mathematics, and more specifically in homological algebra, the splitting lemma states that in any abelian category, the following statements for short exact sequence are equivalent. Given a short exact sequence with maps q and r: :0 ightarrow… …32

**Mayer–Vietoris sequence**— In mathematics, particularly algebraic topology and homology theory, the Mayer–Vietoris sequence is an algebraic tool to help compute algebraic invariants of topological spaces, known as their homology and cohomology groups. The result is due to… …33

**Mitchell's embedding theorem**— Mitchell s embedding theorem, also known as the Freyd–Mitchell theorem, is a result stating that every abelian category admits a full and exact embedding into the category of R modules. This allows one to use element wise diagram chasing proofs… …34

**Nicomachean Ethics**— Part of a series on Aristotle …35

**Spectral sequence**— In the area of mathematics known as homological algebra, especially in algebraic topology and group cohomology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a… …36

**Comte and positivism**— Robert Brown COMTE’S AIMS The chief aim of all of Auguste Comte’s publications, and the constant mission of his entire working life, was the improvement of human character through the perfecting of human society. He was convinced that the… …37

**truth**— I (New American Roget s College Thesaurus) Conformity to fact Nouns 1. truth, fact, reality; verity, gospel, authenticity; plain, unvarnished, sober, or naked truth, matter of fact; the Gospel or naked truth; the truth, the whole truth and… …38

**correctness**— I (Roget s IV) n. 1. [Accuracy] Syn. precision, exactness, exactitude; see accuracy 2 , truth 1 . 2. [Propriety] Syn. decency, decorum, rightness; see fitness 1 , propriety 1 . II (Roget s Thesaurus II) noun 1. Freedom from error: accuracy,… …39

**precision**— I (Roget s IV) n. Syn. exactness, correctness, sureness; see accuracy 2 . II (Roget s 3 Superthesaurus) n. exactness, accuracy, perfection, correctness, fidelity, faithfulness, rectitude, *Swiss watch accuracy, attention to detail. ANT.:… …40

**Justness**— Just ness, n. The quality of being just; conformity to truth, propriety, accuracy, exactness, and the like; justice; reasonableness; fairness; equity; as, justness of proportions; the justness of a description or representation; the justness of a …