monoid object

Equipped with maps \(\ mu: M^{\otimes 2}\to M\) and \(\eta: \one \to M\) Associative:

Left and right unital: % https://q.uiver.app/?q=WzAsNCxbMiwyLCJNIl0sWzIsMCwiTV57XFx0ZW5zb3IgMn0iXSxbMCwwLCJcXG9uZSBcXHRlbnNvciBNIl0sWzQsMCwiTVxcdGVuc29yIFxcb25lIl0sWzIsMSwiXFxldGEgXFx0ZW5zb3IgXFxpZCJdLFsyLDAsIlxcbGFtYmRhIiwyXSxbMSwwLCJcXG11Il0sWzMsMCwiXFxyaG8iXSxbMywxLCJcXGlkXFx0ZW5zb3IgXFxldGEiLDJdXQ==

Monoid structure is preserved by lax monoidal functors.