Tiny objects are closed under finite products
= Tiny objects are closed under finite products
In a <Cartesian closed category>, exponentiation satisfies $(-)^{A\times B}\cong((-)^B)^A$. If the two exponential functors have <right adjoints>, their composite has the composite of those right adjoints in reverse order. Therefore a product of <tiny objects> is tiny. The <terminal object> is tiny since exponentiation by it is the identity, covering the empty product.