- {\displaystyle Mi}
forms a
cofibrant replacement. In fact, if we work in just the
category of
topological spaces, the
cofibrant replacement for any map from...
-
resolving the
source projectively or the
target injectively.
These are
cofibrant or
fibrant replacements in the
respective model structures. The category...
-
particular morphisms), the “fibrant” and “
cofibrant” objects, and
every object is
weakly equivalent to a fibrant-
cofibrant “resolution.”
Although originally developed...
- Kan. They are the Kan
fibrations over a point.
Dually is the
notion of
cofibrant object,
defined to be an
object c {\displaystyle c} such that the unique...
-
subject of
shape theory. In any
model category, a weak
equivalence between cofibrant-fibrant
objects is a
homotopy equivalence.[clarification needed] J. H...
- that a left (right)
Quillen functor preserves weak
equivalences between cofibrant (fibrant) objects. The
total derived functor theorem of
Quillen says that...
- "freeness" to
allow things only to hold up to
homotopy (succinctly: any
cofibrant replacement of the ****ociative operad). An A ∞ {\displaystyle A_{\infty...
- schemes). Example: Let R be a
simplicial commutative ring, Q(R) → R be a
cofibrant replacement, and Ω Q ( R ) 1 {\displaystyle \Omega _{Q(R)}^{1}} be the...
- Let B be an A-algebra, and let M be a B-module. Let P be a
simplicial cofibrant A-algebra
resolution of B. André
notates the qth
cohomology group of B...
- _{*}F\to \pi _{*}G} is an isomorphism. A
sheaf of
spectra is then a fibrant/
cofibrant object in that category. The
notion is used to define, for example, a...
