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1064 Instead, we will give a relatively narrow definition which covers the examples we consider in this paper. |
1064 Instead, we will give a relatively narrow definition which covers the examples we consider in this paper. |
1065 After stating it, we will briefly discuss ways in which it can be made more general. |
1065 After stating it, we will briefly discuss ways in which it can be made more general. |
1066 } |
1066 } |
1067 |
1067 |
1068 Recall the category $\bbc$ of balls with boundary conditions. |
1068 Recall the category $\bbc$ of balls with boundary conditions. |
1069 Note that the morphisms $\Homeo(X;c \to X'; c')$ from $(X, c)$ to $(X', c')$ form a topological space. |
1069 Note that the set of morphisms $\Homeo(X;c \to X'; c')$ from $(X, c)$ to $(X', c')$ is a topological space. |
1070 Let $\cS$ be an appropriate $\infty$-category (e.g.\ chain complexes) |
1070 Let $\cS$ be an appropriate $\infty$-category (e.g.\ chain complexes) |
1071 and let $\cJ$ be an $\infty$-functor from topological spaces to $\cS$ |
1071 and let $\cJ$ be an $\infty$-functor from topological spaces to $\cS$ |
1072 (e.g.\ the singular chain functor $C_*$). |
1072 (e.g.\ the singular chain functor $C_*$). |
1073 |
1073 |
1074 \begin{axiom}[\textup{\textbf{[$A_\infty$ replacement for Axiom \ref{axiom:extended-isotopies}]}} Families of homeomorphisms act in dimension $n$.] |
1074 \begin{axiom}[\textup{\textbf{[$A_\infty$ replacement for Axiom \ref{axiom:extended-isotopies}]}} Families of homeomorphisms act in dimension $n$.] |