Year: 2024
Type: preprint
Abstract: Given an operad $\mathcal{O}$, we define a notion of weak $\mathcal{O}$-monoids -- which we term $\mathcal{O}$-pseudomonoids -- in a 2-category. In the special case with the 2-category in question is the 2-category $\mathsf{Cat}$ of categories, this yields a notion of $\mathcal{O}$-monoidal category, which in the case of the associative and commutative operads retrieves unbiased notions of monoidal and symmetric monoidal categories, respectively. We carefully unpack the definition of $\mathcal{O}$-monoids in the 2-categories of discrete fibrations and of category-indexed sets. Using the classical Grothendieck construction, we thereby obtain an $\mathcal{O}$-monoidal Grothendieck construction relating lax $\mathcal{O}$-monoidal functors into Set to strict $\mathcal{O}$-monoidal functors which are also discrete fibrations.
Source: arXiv (Cornell University)
Authors: Haderi, Redi, Stern, Walker H.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4393734622