Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
The entry cofibration is need of some attention. It wasn’t even linked to from codiscrete cofibration, so I’ve remedied that. There’s also Hurewicz cofibration to bring into the fold.
so then best to add a section with Examples
Would it be OK just to dualise the opening to fibration?
In classical homotopy theory, a fibration $p:E\to B$ is a continuous function between topological spaces that has a certain lifting property. The most basic property is that given a point $e\in E$ and a path $[0,1] \to B$ in $B$ starting at $p(e)$, the path can be lifted to a path in $E$ starting at $e$.
So
In classical homotopy theory, a cofibration $i:A\to B$ is a continuous function between topological spaces that has a certain extension property.
Then?
If the concept of fibration is specified, then the cofibrations are the maps that have the left lifting property again those fibrations that are also weak equivalences. And conversely, if the cofibrations are pre-specified, then the fibrations are those that have the right lifting property against the cofibrations that are also weak equivalences.
A classical example of cofibrations in topology are the Hurewicz cofibrations which are defined by a certain homotopy extension property.
Classically cofibrations were defined in various ways and the idea was independent (and pre-dated) any ideas from model category speak. Of course, once one has that class of maps one can get a useful class of ‘fibrations’, but the concept does not require that and for instance in any setting having a well behaved cylinder one has a well behaved notion of cofibration, but fibrations are not as easy to describe.
1 to 5 of 5