Objects don't matter

[timelets]

Reading McLane & Moerdijk helped me understand that in CT objects don't matter. In most introductory CT books their authors go out of their way to say that CT can handle many useful objects, including sets, etc. In ML&M they cut through the chase in their Categorical Preliminaries



It's clear that object C works in the axioms as a placeholder, it is used briefly to denote any kind of object. What really matters is the structure of functions and rules to construct them.