%
%
% Global definitions *****************
%
% Functors, Hom, End, Ext, ....
%
\newcommand{\Hom}{\operatorname{Hom}\nolimits} 
\newcommand{\uHom}{\operatorname{\underline{Hom}}\nolimits}
\newcommand{\oHom}{\operatorname{\overline{Hom}}\nolimits}
\newcommand{\End}{\operatorname{End}\nolimits}
\newcommand{\uEnd}{\operatorname{\underline{End}}\nolimits}
\newcommand{\oEnd}{\operatorname{\overline{End}}\nolimits}
\newcommand{\Irr}{\operatorname{Irr}\nolimits}
\newcommand{\Aut}{\operatorname{Aut}\nolimits}
\newcommand{\rad}{\operatorname{rad}\nolimits}
\newcommand{\soc}{\operatorname{soc}\nolimits}
\newcommand{\ann}{\operatorname{ann}\nolimits}
\newcommand{\Tor}{\operatorname{Tor}\nolimits}
\newcommand{\Ext}{\operatorname{Ext}\nolimits}
\newcommand{\Tr}{\operatorname{Tr}\nolimits}
%
% Categories, subcategories
%
\renewcommand{\mod}{\operatorname{mod}\nolimits}
\newcommand{\Mod}{\operatorname{Mod}\nolimits}
\newcommand{\ind}{\operatorname{ind}\nolimits}
\newcommand{\umod}{\operatorname{\underline{mod}}\nolimits}
\newcommand{\omod}{\operatorname{\overline{mod}}\nolimits}
\newcommand{\Morph}{\operatorname{Morph}\nolimits}
\newcommand{\Sub}{\operatorname{Sub}\nolimits}
\newcommand{\Fac}{\operatorname{Fac}\nolimits}
\newcommand{\Supp}{\operatorname{Supp}\nolimits}
\newcommand{\Ab}{\operatorname{Ab}\nolimits}
\newcommand{\add}{\operatorname{add}\nolimits}
\newcommand{\Rep}{\operatorname{Rep}\nolimits}
%
% Objects, kernel, cokernel, images, etc.
%
\renewcommand{\Im}{\operatorname{Im}\nolimits}
\newcommand{\Ker}{\operatorname{Ker}\nolimits}
\newcommand{\Coker}{\operatorname{Coker}\nolimits}
\newcommand{\Spec}{\operatorname{Spec}\nolimits}
\newcommand{\Gl}{\operatorname{Gl}\nolimits}
\newcommand{\Sl}{\operatorname{Sl}\nolimits}
%
% Dimensions, rank, etc.
%
\newcommand{\pd}{\operatorname{pd}\nolimits}
\newcommand{\id}{\operatorname{id}\nolimits}
\newcommand{\domdim}{\operatorname{dom.dim}\nolimits}
\newcommand{\rank}{\operatorname{rank}\nolimits}
\newcommand{\depth}{\operatorname{depth}\nolimits}
\newcommand{\length}{\operatorname{\ell}\nolimits}
\renewcommand{\dim}{\operatorname{dim}\nolimits}
\newcommand{\udim}{\operatorname{\underline{dim}}\nolimits}
\newcommand{\findim}{\operatorname{fin.dim}\nolimits}
\newcommand{\gldim}{\operatorname{gl.dim}\nolimits}
\newcommand{\kar}{\operatorname{char}\nolimits}
%
% Ideals
\newcommand{\m}{\operatorname{\underline{m}}\nolimits}
\renewcommand{\r}{\operatorname{\underline{r}}\nolimits}
%
% Misecellaneous
%
\newcommand{\op}{{\operatorname{op}}} 
\renewcommand{\c}[1]{\mathcal #1}
\newcommand{\bbb}[1]{\mathbb #1}
\newcommand{\Sets}{\operatorname{Sets}\nolimits}
%



