Monoidal functor (source code)

= Monoidal functor

= Lax monoidal functor
{synonym}

Here the unqualified term allows lax comparison maps $F_2:FX\otimes FY\to F(X\otimes Y)$ and $F_0:I\to FI$, natural and compatible with <associators> and <unitors>. Invertible comparison maps give a <strong monoidal functor>. The opposite direction gives an <opmonoidal functor>.