notations.tex

% -*- coding:utf-8 -*-
\renewcommand{\nomname}{Notations}
\nomenclature{$\forall$}{for all}
\nomenclature{$\exists$}{exists}
%\nomenclature{\(\exists"!\)}{exists exactly one}
\nomenclature{$\Ima{f}$}{\mynameref{def:function_image} of the function $f$}
\nomenclature{$\cat{Set}$}{\mynameref{def:setcategory}}
\nomenclature{$\cat{Rel}$}{\mynameref{def:relcategory}}
\nomenclature{$\cat{Proof}$}{\mynameref{def:proof_category}}
\nomenclature{$\cat{FdHilb}$}{\mynameref{def:fdhilbcategory}}
\nomenclature{$\cat{Hask}$}{\mynameref{def:haskcategory}}
\nomenclature{$\cat{Scala}$}{\mynameref{def:scalacategory}}
\nomenclature{$\cat{C\texttt{++}}$}{\mynameref{def:cppcategory}}
\nomenclature{$\cat{Cat}$}{\mynameref{def:catcategory}}
\nomenclature{$a, b$}{\mynameref{def:object}s (Latin small letters)}
\nomenclature{$f, g, h$}{\mynameref{def:morphism}
  (\mynameref{def:arrow}) (Latin small letter)}
\nomenclature{$a \times b$}{\mynameref{def:product}}
\nomenclature{$a \oplus b$}{\mynameref{def:sum}}
\nomenclature{$f: a \to b$}{\mynameref{def:morphism} (simple arrow)}
\nomenclature{$f: a \hookrightarrow b$}{\mynameref{def:monomorphism}
  (hook arrow)}
\nomenclature{$f \circ g$}{Morphism composition (circle dot)}
\nomenclature{$\cat{C}$}{\mynameref{def:category} (bold capital Latin
  letter)}
\nomenclature{$\cat{C}^{op}$}{\mynameref{def:op_category}}
\nomenclature{$\idm{a}$}{\mynameref{def:id}}
\nomenclature{$\idf{C}$}{\mynameref{def:idfunctor}}
\nomenclature{$F, G$}{\mynameref{def:functor}
  (capital Latin letter)}
\nomenclature{$\dom f$}{\mynameref{def:domain}}
\nomenclature{$\cod f$}{\mynameref{def:codomain}}
\nomenclature{$F: \cat{C} \tof \cat{D}$}{\mynameref{def:functor}
  (double arrow)}
\nomenclature{$F \circ G$}{\mynameref{def:functor_composition} (circle
  dot)}
\nomenclature{$\Delta_c$}{\mynameref{def:const_functor}}
\nomenclature{$\alpha, \beta$}{\mynameref{def:nt}
 (Greek small letters)}
\nomenclature{$\alpha: F \tont G$}{\mynameref{def:nt}
(arrow with dot)}
\nomenclature{$\funcat{C}{D}$}{\mynameref{def:funcategory}}
\nomenclature{$\alpha \circ
  \beta$}{\mynameref{def:vertical_composition} of natural
  transformations (circle dot)}
\nomenclature{$\alpha \star \beta$}{\mynameref{def:horizontal_composition} of natural transformations (star dot)}
\nomenclature{$\alpha H$}{\mynameref{def:lw}}
\nomenclature{$H \alpha$}{\mynameref{def:rw}}
\nomenclature{$\idnt{F}$}{\mynameref{def:idnt}}
\nomenclature{$a \cong_f b$}{there is an \mynameref{def:isomorphism} $f$
  between $a$ and $b$} 
\nomenclature{$a \cong b$}{there is an \mynameref{def:isomorphism} 
  between $a$ and $b$. The exact isomorphism does not matter in the case} 
\nomenclature{$\left<M, \mu, \eta\right>$}{\mynameref{def:monad}}
\nomenclature{$\cat{C_M}$}{\mynameref{def:kleisli_category}}
\nomenclature{$\catmset{a}{b}$}{\mynameref{def:morphism_set} between $a$ and $b$}
\nomenclature{$\catmset[C]{a}{b}$}{\mynameref{def:morphism_set}
  between $a$ and $b$ in category $\cat{C}$}
\nomenclature{$\mathcal{H}_n$}{finite dimensional
  \mynameref{def:hilbert_space}}
\nomenclature{$a^b$}{\mynameref{def:exponential}}
\nomenclature{$P \implies Q$}{\mynameref{def:implication}}
\nomenclature{$\catcone{c}{f}$}{\mynameref{def:cone}}
\nomenclature{$\catcocone{c}{f}$}{\mynameref{def:cocone}}
\nomenclature{$\Delta \downarrow
  F$}{\mynameref{def:category_of_cones}}
\nomenclature{$F \downarrow
  \Delta$}{\mynameref{def:category_of_cocones}}
\nomenclature{$eq\left(f, g\right)$}{\mynameref{def:equalizer}}
\nomenclature{$\catcovhom{C}{a}$}{\mynameref{def:cov_hom_functor}}
\nomenclature{$\catconhom{C}{a}$}{\mynameref{def:con_hom_functor}}
%% https://tex.stackexchange.com/questions/31562/nomencl-package-and-vertical-bar
\nomenclature{$\lvert A \rvert$ }{\mynameref{def:cardinality} of a
  \mynameref{def:set} $A$} 
\nomenclature{$curry(f)$ }{\mynameref{def:currying_set}} 
\nomenclature{TBD}{To Be Defined (later)}

\printnomenclature