equality of natural transformations? Sean $F,G:C\longrightarrow{D}$ dos funtores.
Ahora sean dos transformaciones naturales $r, s:F\longrightarrow{G}$.
Preguntas:
Cuándo $r$ y $s$ son isomorfos ? quiero una definición usando objetos o flechas.
Cuándo $r=s$ ?
Siempre  una aplicación entre funtores  $t:F\longrightarrow{G}$ es transformación natural ?
Gracias

Hi.
 
Let $F,G:C\longrightarrow{D}$ be two functors.
Now let $r, s:F\longrightarrow{G}$ be two natural transformations
Questions:
When are $ r $ and $ s $ are isomorphic? I want a definition using objects or arrows.
When is $ r = s $?
Always an application between functors $t:F\longrightarrow{G}$ is natural transformation?
 A: In any category, two objects, $A$ and $B$, are isomorphic iff there exists two arrows, $h$ and $k$, such that $h\circ k = id_A$ and $k \circ h = id_B$. The definition of "isomorphic" is always the same. What changes is the category it's being applied to.
However, natural transformations are not normally considered objects of a category and you haven't specified a category, so it doesn't make sense to ask when two natural transformations are isomorphic. You could trivially turn a set of natural transformations into a discrete category at which point they'd be isomorphic iff they are equal.
Category theory is usually formulated within some ambient set theory, and that set theory usually has a global notion of equality. Nevertheless, we can be a bit more specific. Two natural transformations are equal iff they are equal component-wise. In symbols, $$r = s \iff \forall A\in\mathsf{Ob}(\mathcal{C}).r_A = s_A$$ $r_A$ and $s_A$ are arrows of $\mathcal{D}$ and when arrows are equal is information you provide when you define a category (assuming you aren't just relying on a global notion of equality).
