- {\displaystyle C_{f}} . Alternatively, it is also
called the
homotopy cofiber and also
notated C f {\displaystyle Cf} . Its dual, a fibration, is called...
- replacement. For a
cofibration A → X {\displaystyle A\to X} we
define the
cofiber to be the
induced quotient space X / A {\displaystyle X/A} . In general...
- In
category theory, a
branch of mathematics, a
pushout (also
called a
fibered coproduct or
fibered sum or
cocartesian square or
amalgamated sum) is the...
- {\displaystyle C(f)}
denote a
mapping cone of f, (i.e., the
cofiber of the map f), so that we have a (
cofiber) sequence: A → B → C ( f ) {\displaystyle A\to B\to...
-
exact sequences in an
abelian category, as well as
fiber sequences and
cofiber sequences in topology. Much of
homological algebra is
clarified and extended...
-
morphism in it
admits a
fiber and
cofiber. (iii) A
triangle in it is a
fiber sequence if and only if it is a
cofiber sequence. The
homotopy category of...
-
sequence of
homotopy groups.
There is a dual
construction called the
homotopy cofiber. The
homotopy fiber has a
simple description for a
continuous map f : A...
- for the
cofiber of τ as the
algebraic Novikov spectral sequence for BP*,
which allows one to
deduce motivic Adams differentials for the
cofiber of τ from...
- (X,\Omega Y).}
These functors are used to
construct fiber sequences and
cofiber sequences. Namely, if f : X → Y {\displaystyle f:X\to Y} is a map, the...
- \mathbb {L} _{R}\to \mathbb {L} _{S}} . Then, for each R → S,
there is the
cofiber sequence of S-modules L S / R → L R ⊗ R L S → L S . {\displaystyle \mathbb...
