- In mathematics, an
exact sequence is a
sequence of
morphisms between objects (for example, groups, rings, modules, and, more generally,
objects of an abelian...
-
exact sequence,
built from the
mapping fibre (a fibration), and a long
coexact sequence,
built from the
mapping cone (which is a cofibration). Intuitively...
- needed] via the
Hodge decomposition theorem as the sum of an exact, a
coexact, and a
harmonic form, A = d α + δ β + γ {\displaystyle A=d\alpha +\delta...
-
cofibration is the
mapping cone, then the
resulting exact (or dually,
coexact)
sequence is
given by the
Puppe sequence.
There are many
realizations of...
- of currying,
which in turn
leads to the
duality of the long
exact and
coexact Puppe sequences. In
homological algebra, the
relationship between currying...
- H_{*}(C_{f},pt)=0} .
Mapping cones are
famously used to
construct the long
coexact Puppe sequences, from
which long
exact sequences of
homotopy and relative...
- ^{2}A\to \cdots .\,} and more generally, the
duality between the
exact and
coexact Puppe sequences. This also
allows us to
relate homotopy and cohomology:...
- \in \Omega ^{k-1}}
coclosed if δ α = 0 {\displaystyle \delta \alpha =0}
coexact if α = δ β {\displaystyle \alpha =\delta \beta } for some β ∈ Ω k + 1 {\displaystyle...
-
pairwise orthogonal spaces, the
closure of
exact 1-forms df, the
closure of
coexact 1-forms ∗df and the
harmonic 1-forms (the 2-dimensional
space of constant...
