Let $Mon$ (resp., $CMon$) be a category of monoids (resp., commutative monoid) whose morphisms are usual monoid homomorphisms (resp., commutative monoid homomorphism). Is this category complete and/or cocomplete? If you know, could you give me any reference for this fact?
What I found currently is this answer and the author claims that both categories are complete/cocomplete for all small limits/colimits. However, I have difficulties finding references for this fact.