Functors and related things:

1. $\pi_1(X, x_0)$ the fundamental group of $X$ with base point $x_0$
2. $H_n(X)$ the $n-$th homology group of $X$
3. $H_n(X, A)$ the $n-$th relative homology group of the pair $(X, A)$
4. $Z_n(X)$ the group of singular $n-$cycles in $X$

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