diff --git a/2021_Algebra_I.tex b/2021_Algebra_I.tex index a3331d3..6e0be69 100644 --- a/2021_Algebra_I.tex +++ b/2021_Algebra_I.tex @@ -2305,9 +2305,9 @@ If $P_e $ with $e < d$ was $\neq 0$, it could not be a multiple of $P$ contradic The bijectivity of the $\phi_{U, (U_i)_{i \in I}}$ is called the \vocab{sheaf axiom}. \end{definition} -\begin{dtrivial} +\begin{trivial}+ A presheaf is a contravariant functor $\mathcal{G} : \mathcal{O}(X) \to C$ where $\mathcal{O}(X)$ denotes the category of open subsets of $X$ with inclusions as morphisms and $C$ is the category of sets, rings or (abelian) groups. -\end{dtrivial} +\end{trivial} \begin{definition} A subsheaf $\mathcal{G}'$ is defined by subsets (resp. subrings or subgroups) $\mathcal{G}'(U) \subseteq \mathcal{G}(U)$ for all open $U \subseteq X$ such that the sheaf axioms still hold. \end{definition}