cofibration
Sign in to saveIn mathematics, in particular homotopy theory, a continuous mapping between topological spaces
~7 min read
Article
12 sectionsContents
- Definition
- Homotopy theory
- Examples
- In topology
- In chain complexes
- Simplicial sets
- Properties
- Constructions with cofibrations
- Cofibrant replacement
- Cofiber
- See also
- References
In mathematics, in particular homotopy theory, a continuous mapping between topological spaces i: A \to X
is a cofibration if it has the homotopy extension property with respect to all topological spaces S. That is, i is a cofibration if for each topological space S, and for any continuous maps f, f': A\to S and g:X\to S with g\circ i=f, for any homotopy h : A\times I\to S from f to f', there is a continuous map g':X \to S and a homotopy h': X\times I \to S from g to g' such that h'(i(a),t)=h(a,t) for all a\in A and t\in I. (Here, I denotes the unit interval [0,1].)
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