Given a functor between categories, how to denote a morphism between particular objects of that category
I have a very common situation, for which I need both: (1) notation; and, if available, (2) a general relative term. Let's say that: there is a functor between categories, $f:C_1\to C_2$, $c_1$ is ...
Let $X$ be a set and let $A$ be a subet of $X$. Let $i:A\longrightarrow X$ be the usual inclusion of $A$ in $X$. Then $i$ is an example of an injective function. I want to show that every ...
A surjection is a function whose range equals its codomain. Thus, the distinction between functions and surjections requires the notion of a codomain. Similarly, a bijection is an injection whose ...