Cofibrations in the Category of Frolicher Spaces. Part I

Cofibrations are defined in the category of Fr"olicher spaces by weakening the analog of the classical definition to enable smooth homotopy extensions to be more easily constructed, using flattened unit intervals. We later relate smooth cofibrations to smooth neighborhood deformation retracts. The notion of smooth neighborhood deformation retract gives rise to an analogous result that a closed Fr"olicher subspace $A$ of the Fr"olicher space $X$ is a smooth neighborhood deformation retract of $X$ if and only if the inclusion $i: A\hookrightarrow X$ comes from a certain subclass of cofibrations. As an application we construct the right Puppe sequence.

💡 Research Summary

The paper develops a theory of cofibrations within the category of Frölicher spaces, which are smooth spaces defined by a compatible pair of smooth curves and smooth real‑valued functions. In classical topology a cofibration is an inclusion that satisfies the homotopy extension property (HEP). Directly transferring this definition to Frölicher spaces fails because the usual unit interval (