nLab m-commutative monoid

Definition

Definition

If $\mathcal{C}$ is a complete (∞,1)-category, then the ∞-category of $m$-commutative monoids in $\mathcal{C}$ is

$$\mathrm{CMon}_m(\mathcal{C}) := \mathrm{Fun}^{m-\mathrm{fin}}(\mathrm{Span}(\mathcal{S}_m)^{\op},\mathcal{C}),$$

where $\mathrm{Fun}^{m-\mathrm{fin}}$ refers to the category of functors which preserve (∞,1)-limits indexed by m-finite spaces.

Related concepts

• semiadditive (∞,1)-category

• m-finite space

References

• Yonatan Harpaz, Ambidexterity and the universality of finite spans (2017) (arXiv:1703.09764)

• Shachar Carmeli?, Tomer Schlank, Lior Yanovski, Ambidexterity and Height (2020) (arXiv:2007.13089)