# exactness

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**Auguste Comte**— Isidore Auguste Marie François Xavier Comte Full name Isidore Auguste Marie François Xavier Comte Born 19 January 1798 Montpellier, France Died September 5, 1857( …52

**Hume's principle**— Hume s Principle, or HP the terms were coined by George Boolos mdash;says that the number of F s is equal to the number of G s if there is a one to one correspondence (a bijection) between the F s and the G s. HP can be stated formally in systems …53

**Projective module**— In mathematics, particularly in abstract algebra and homological algebra, the concept of projective module over a ring R is a more flexible generalisation of the idea of a free module (that is, a module with basis vectors). Various equivalent… …54

**Exact functor**— In homological algebra, an exact functor is a functor, from some category to another, which preserves exact sequences. Exact functors are very convenient in algebraic calculations, roughly speaking because they can be applied to presentations of… …55

**Spin structure**— In differential geometry, a spin structure on an orientable Riemannian manifold allows one to define associated spinor bundles, giving rise to the notion of a spinor in differential geometry. Spin structures have wide applications to mathematical …56

**Thai Prophecy Verse**— (th: เพลงยาวพยากรณ์กรุงศรีอยุธยา, RTGS: Phleng yao phayakon krung si ayutthaya, the verse prophesying the future of Krung Si Ayutthaya) is a poetry forecasting the future of Thailand. It was composed on a par with Maha Supina Jataka in Tripitaka …57

**Philosophy of healthcare**— The philosophy of healthcare is the study of the ethics, processes, and people which constitute the maintenance of health for human beings. (Although veterinary concerns are worthy to note, the body of thought regarding their methodologies and… …58

**Cotangent complex**— In mathematics the cotangent complex is a roughly a universal linearization of a morphism of geometric or algebraic objects. Cotangent complexes were originally defined in special cases by a number of authors. Luc Illusie, Daniel Quillen, and M.… …59

**Aggregated Indices Randomization Method**— (AIRM) is a modification of well known aggregated indices method being aimed at complex objects multi criteria estimation under uncertainty. The main advantage of AIRM over other variants of aggregated indices methods is its ability to use non… …60

**Zig-zag lemma**— In mathematics, particularly homological algebra, the zig zag lemma asserts the existence of a particular long exact sequence in the homology groups of certain chain complexes. The result is valid in every abelian category. Statement In an… …