I am reading a paper about persistent homology and was wondering if anyone knows what the meaning of function composition, $\circ$, is in this context?
The persistent module, $M$, is the algebraic object of interest in TDA. It consists of vector space $M_a$ for $a \in \mathbb{R}$ and linear maps $M(a \le b): M_a \rightarrow M_b$ for all $a \le b$ such that $M(a \le a)$ is the identify map so that for all $a \le b \le c$ it is that $M(b \le c) \circ M(a \le b) = M(a \le c)$.