TikZ - Style for arrow with midpoint decorator

Question

I am creating a kind of commutative diagram with different types of arrows. So far, I have defined different line styles for my different types of map, like this:

\tikzstyle{map}=[->,>=stealth',semithick]
\tikzstyle{incmap}=[semithick, right hook-latex]
\tikzstyle{typemap}=[->,>=latex',thin, dashed]

This way, I declare all my nodes in the layout that I want, and then I can declare maps between them easily using \draw[<style>]. In addition, I can easily switch the style of a map (e.g. from a inclusion map to a normal one) if I decide that it is not the correct one.

Now, I want to create an arrow style for partial maps that looks like a normal arrow with a circle in the midpoint (no matter the length of the arrow). I know that I can do this in a one-by-one fashion, but I would like to be able to define that in a style, in a similar way to the others. To clarify, the arrows should look like this:

-o->
--o-->
---o--->

Any suggestions?

I am not using TikZ's cd library, but I have checked it and there is nothing that solves the problem.

Thanks in advance!

EDIT: As suggested, I add here the MWE with my initial status.

\documentclass{standalone}
\usepackage{tikz}

\usetikzlibrary{arrows,positioning,shapes}

\begin{document}
\begin{tikzpicture}[on grid,node distance=20mm]

\tikzstyle{element}=[inner sep=2pt,minimum height=1.3em,font=\itshape]
\tikzstyle{label}=[auto,midway,font=\itshape,inner sep=2pt]
\tikzstyle{map}=[->,>=stealth',semithick]
\tikzstyle{incmap}=[semithick, left hook-latex]
\tikzstyle{typemap}=[->,>=latex',thin, dashed]

\node[element] (l)  []  {L};
\node[element] (i)  [right of=l]    {I};
\node[element] (r)  [right of=i]    {R};

\draw[map]      (l) to node [label,above]   (lm)    {l}     (i);
\draw[incmap]   (r) to node [label,above]   (rm)    {r}     (i);

\end{tikzpicture}
\end{document}

Answer 1

Using markings worked perfectly. Here is how I solved it:

\documentclass{standalone}
\usepackage{tikz}

\usetikzlibrary{arrows,positioning,shapes,decorations.markings}

\begin{document}
\begin{tikzpicture}[on grid,node distance=20mm,
  decoration={markings,mark=at position 0.5 with {\draw circle [radius=.4ex];}}]

\tikzset{element/.style={inner sep=2pt,minimum height=1.3em,font=\itshape}}
\tikzset{label/.style={auto,midway,font=\itshape,inner sep=2pt}}
\tikzset{map/.style={->,>=stealth',semithick}}
\tikzset{incmap/.style={semithick, left hook-latex}}
\tikzset{partmap/.style={->,>=latex,semithick,postaction={decorate}}}

\node[element] (l)  []  {L};
\node[element] (i)  [right of=l]    {I};
\node[element] (r)  [right of=i]    {R};

\draw[partmap]  (l) to node [label,above]   (lm)    {l}     (i);
\draw[incmap]   (r) to node [label,above]   (rm)    {r}     (i);

\end{tikzpicture}
\end{document}

Thanks again to the people who answered!