stuff

_chapters/01_set.md

@@ -522,7 +522,7 @@ When you do that, it would be important to highlight that you are not referring
 
 ![A set of two balls](../01_set/number_two_sets.svg)
 
-This is a good starting point, but the person may still be staring at the objects instead of the structure — they might ask if this or that set is $2$ as well. At this point you might give up, or, if the person whom you are explaining happens to know about isomorphisms as well (let's say they lived in a cave with nothing but this book with them), you can easily formulate your final definition, saying that the number $2$ is represented by those sets and all other sets that are isomorphic to them, or by the *equivalence class* of sets that have two elements, as the formal definition goes (don't worry, we will learn all about equivalence classes later).
+This is a good starting point, but the person may still be staring at the objects instead of the structure — they might ask if this or that set is $2$ as well. At this point, if the person whom you are explaining happens to know about isomorphisms (let's say they lived in a cave with nothing but this book with them), you can easily formulate your final definition, saying that the number $2$ is represented by those sets and all other sets that are isomorphic to them, or by the *equivalence class* of sets that have two elements, as the formal definition goes (don't worry, we will learn all about equivalence classes later).
 
 ![A set of two balls](../01_set/number_two_isomorphism.svg)
 

_chapters/02_category.md

@@ -98,6 +98,7 @@ Suggested in 1921 Kazimierz Kuratowski, this one uses just the component of the
 Defining products in terms of functions 
 ---
 
+
 In the product definitions presented in the previous section worked by *zooming in* into the individual elements of the product and seeing what they can be made of We may think of this as a *low-level* approach to the definition. This time we will try to do the opposite --- we will try to be as oblivious to the contents of our sets as possible i.e. instead of zooming in we will *zoom out*, we will attempt to fly over the difficulties that we met in the previous section and provide a definition of a product in terms of functions and *external* diagrams.
 
 How can we define products in terms of external diagrams i.e. given two sets how can we pinpoint the set that is their product? To do that, we must first think about *what functions* are there for a given product, and we have two of those --- the functions for retrieving the two elements of the pair (the "getters", so to say).