United Monoids | no time

In this blog post we will explore the consequences of postulating 0 = 1 in an algebraic structure with two binary operations (S, +, 0) and (S, ⋅, 1). Such united monoids have a few interesting properties, which are not immediately obvious. For example, we will see that the axiom 0 = 1 is equivalent to a seemingly less extravagant axiom ab = ab + a, which will send us tumbling down the rabbit hole

[lotz84]

2つのモノイド構造を持ち0=1を満たすやつ。逆元を取る操作が無いから環の時のように0には潰れない。algebraic-graphのOverlayとConnectがこの性質を持つ。単体的複体も例に上がってるのが面白い