Cofibrant space

In mathematics , a topological space is called cofibrant if the inclusion is a cofiber for each point . For example, CW complexes are cofibrant spaces. ${\displaystyle x\in X}$ ${\displaystyle \left\{x\right\}\to X}$

A cofibrant approximation (or cofibrant resolution ) of a topological space is a cofibrant space with weak homotopy equivalence . ${\displaystyle X}$ ${\displaystyle {\widetilde {X}}}$ ${\displaystyle i\colon {\widetilde {X}}\to X}$

literature

• Philip S. Hirschhorn: Model categories and their localizations. Mathematical Surveys and Monographs, 99. American Mathematical Society, Providence, RI, 2003. ISBN 0-8218-3279-4
• Paul Balmer, Michel Matthey: Codescent theory. II. Cofibrant approximations. Homology, Homotopy Appl. 8 (2006), no. 1, 211-242.