Just testing around with clean functional react components and the question how to get state in a stateless function. The answer is composition.

Counter.jsx

import React from 'react';
import PropTypes from 'prop-types';

const propTypes = {
    count: PropTypes.number.isRequired,
    onIncrement: PropTypes.func.isRequired,
    onDecrement: PropTypes.func.isRequired,
};

const Counter = ({ count, onIncrement, onDecrement }) => (
    <div>
        <span>{count}</span>
        <button onClick={onIncrement}>Increment</button>
        <button onClick={onDecrement}>Decrement</button>
    </div>
);

Counter.propTypes = propTypes;

export default Counter;

GlobalCounter.js

import PropTypes from 'prop-types';
import { connect } from 'react-redux';
import { selectCount } from './selectors';
import { increment, decrement } from './actions';
import Counter from './Counter';

const mapStateToProps = state => ({
    count: selectCount(state),
});

const mapDispatchToProps = dispatch => ({
    onIncrement: () => dispatch(incremet()),
    onDecrement: () => dispatch(decremet()),
});

export default connect(
  mapStateToProps,
  mapDispatchToProps,
)(Counter);

LocalCounter.js

import PropTypes from 'prop-types';
import {
    compose,
    onlyUpdateForPropTypes,
    setPropTypes,
    withHandlers,
    withState,
} from 'recompose';
import Counter from './Counter';

const propTypes = {
    startCount: PropTypes.number.isRequired,
};

export default compose(
    onlyUpdateForPropTypes,
    setPropTypes(propTypes),
    withState('count', 'updateCounter', ({ startCount = 0 }) => startCount),
    withHandlers({
        onIncrement: props => () => props.updateCounter(props.count + 1),
        onDecrement: props => () => props.updateCounter(props.count - 1),
    }),
)(Counter);