title: Products and coproducts in posets
body: <p>While reading Bartosz' excellent <a href="https://bartoszmilewski.com/2014/10/28/category-theory-for-programmers-the-preface/">Category theory for Programmers</a>, I got stuck in the second exercise, which deals with products in posets. Given a poset,</p>
  
  <pre><code>    b   e
    ↗   ⤭   ↘
  a → c   f → h
    ↘   ⤭   ↗
      d   g
  </code></pre>
  
  <p>how can I define a product in the categorical sense? What is categorized by the product of two objects? And what about the coproduct?</p>