A morphism $f\colon A\to B$ of $\mathcal{C}$ is an isomorphism if there exists a morphism $\smash {f^{-1}\colon B\to A}$ of $\mathcal{C}$ such that
\begin{align*} f\circ f^{-1} & = \text{id}_{B},\\ f^{-1}\circ f & = \text{id}_{A}. \end{align*}
Here's a breakdown of the differences between each PDF style:
Style | Class | Font | Theorem Environments |
---|---|---|---|
Style 1 | book |
Alegreya Sans | tcbthm |
Style 2 | book |
Alegreya Sans | amsthm |
Style 3 | book |
Arno* | amsthm |
Style 4 | book |
Computer Modern | amsthm |
*To be replaced with Linus Romer's Elemaints when it is released.
A morphism $f\colon A\to B$ of $\mathcal{C}$ is an isomorphism if there exists a morphism $\smash {f^{-1}\colon B\to A}$ of $\mathcal{C}$ such that