 A first characteristic assumption is that all mathematical theorems are schematic statements that have a conditional form. This point is explicit in Awodey (2004). We already saw that according to Awodey a category-theoretic approach is non-foundational in character. This includes that mathematical axioms and theorems, as expressed in category theory, should be understood as schematic statements. They do not express truths about the specific nature of mathematical objects, but rather, about their respective properties and relations. In addition, mathematical theorems are, at least in principle, all of hypothetical form. They can be reconstructed as if-then statements. Note that this view of the logical form of mathematical theorems is prima facie similar to the if-then-ism one can find in Putnam’s works, and earlier in Russell’s, as mentioned in section 1.  