Topological half-exact functor
- Topological half-exact functor
In mathematics, a topological half-exact functor "F" is a functor from a fixed topological category (for example CW complexes or pointed spaces) to an abelian category (most frequently in applications, category of abelian groups or category of modules over a fixed ring) that has a following property: for each sequence of the form:
: "X" → "Y" → "C(f)"
where "C(f)" denotes a mapping cone, a sequence:
: "F(X)" → "F(Y)" → "F(C(f))"
is exact.
Examples include functors of homology.
Wikimedia Foundation.
2010.
Look at other dictionaries:
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… … Wikipedia
List of mathematics articles (T) — NOTOC T T duality T group T group (mathematics) T integration T norm T norm fuzzy logics T schema T square (fractal) T symmetry T table T theory T.C. Mits T1 space Table of bases Table of Clebsch Gordan coefficients Table of divisors Table of Lie … Wikipedia
Puppe sequence — In mathematics, the Puppe sequence is a construction of homotopy theory.Let f : A → B be a continuous map between CW complexes and let C(f) denote a cone of f, so that we have a sequence:: A → B → C(f) Now we can form Σ A and Σ B , suspensions of … Wikipedia
Adjoint functors — Adjunction redirects here. For the construction in field theory, see Adjunction (field theory). For the construction in topology, see Adjunction space. In mathematics, adjoint functors are pairs of functors which stand in a particular… … Wikipedia
Boolean algebras canonically defined — Boolean algebras have been formally defined variously as a kind of lattice and as a kind of ring. This article presents them more neutrally but equally formally as simply the models of the equational theory of two values, and observes the… … Wikipedia
List of mathematics articles (F) — NOTOC F F₄ F algebra F coalgebra F distribution F divergence Fσ set F space F test F theory F. and M. Riesz theorem F1 Score Faà di Bruno s formula Face (geometry) Face configuration Face diagonal Facet (mathematics) Facetting… … Wikipedia
List of important publications in mathematics — One of the oldest surviving fragments of Euclid s Elements, found at Oxyrhynchus and dated to circa AD 100. The diagram accompanies Book II, Proposition 5.[1] This is a list of important publications in mathematics, organized by field. Some… … Wikipedia
Epimorphism — In category theory an epimorphism (also called an epic morphism or an epi) is a morphism f : X rarr; Y which is right cancellative in the following sense: : g 1 o f = g 2 o f implies g 1 = g 2 for all morphisms g 1, g 2 : Y rarr; Z .Epimorphisms… … Wikipedia
