<p>I think your question is on the right track but there are so many more ways in which Category Theory connects to other concepts. I also find that relating Category Theory to Type Theory brings more to the table than relating Category Theory to transformations. I say relating, because while Math and Computer Science may use the same terminology, they are not the same; one is not interchangeable with the other.</p>

<h2><a href="https://arxiv.org/pdf/0903.0340v3.pdf" rel="nofollow noreferrer">Physics, Topology, Logic and Computation: A Rosetta Stone</a></h2>

<p>by John C. Baez and Mike Stay</p>

<p>Category Theory: object X<br>
Computation: data type X  </p>

<p>Category Theory: morphism f: X → Y<br>
Computation:  program f: X → Y  </p>

<p>Category Theory: tensor product of objects: X ⊗ Y<br>
Computation: product of data types: X ⊗ Y  </p>

<p>Category Theory: tensor product of morphisms:  f ⊗ g<br>
Computation: programs executing in parallel:  f ⊗ g  </p>

<p>Category Theory: internal hom: X ⊸ Y<br>
Computation: function type: X ⊸ Y  </p>

<h2><a href="https://ncatlab.org/nlab/show/relation+between+type+theory+and+category+theory" rel="nofollow noreferrer">relation between type theory and category theory</a></h2>

<p>from nLab</p>

<p>Category Theory: counit for hom-tensor adjunction<br>
Type Theory: beta reduction  </p>

<p>Category Theory: unit for hom-tensor adjunction<br>
Type Theory: eta conversion  </p>

<h2>Yoneda embedding</h2>

<blockquote>
  <p>The Yoneda embedding is familiar in category theory. The continuation passing transform is familiar in computer programming. 
  <a href="https://golem.ph.utexas.edu/category/2008/01/the_continuation_passing_trans.html" rel="nofollow noreferrer">They’re the same thing!</a> Why doesn’t anyone ever say so?</p>
</blockquote>

<p>by Mike Stay</p>

<h2>Other references</h2>

<p>There is so much more to this question than can possibly be put into an SO answer.</p>

<p>When I was looking into this in the past I asked most of my questions at <a href="https://cs.stackexchange.com/">StackExchange: Computer Science</a> and updated the most useful references as part of the <a href="https://cs.stackexchange.com/tags/category-theory/info">Category Theory tag</a>. Most of what you seek is found in those references.</p>

<h2>TL;DR</h2>

<p>If I could have created tables with the SO Markdown I would have added a lot more, but without being in a table seeing them in a list just loses its impact.</p>

<p>If you find Category Theory of interest, then you should also look at <a href="https://homotopytypetheory.org/book/" rel="nofollow noreferrer">HoTT</a> (Homotopy Type Theory)</p>
Which terms is corresponding for Map, Filter, Foldable, Bind etc from Category Theory?
<p>I became interested and did not find in one place a list of corresponding terms:</p>

<p><code>Map &lt;-&gt; Morphism</code></p>

<p><code>Foldable &lt;-&gt; Catamorphism</code></p>

<p>...</p>

<p>Who can supplement the list of terms</p>