Search Results

$\newcommand{\C}{\mathcal C} \newcommand{\D}{\mathcal D} \newcommand{\F}{\mathcal F} \renewcommand{\H}{\mathcal H} \newcommand{\from}{\colon} \newcommand{\tensor}{\otimes} \require{AMScd}$ Given mono …

Let $\mathcal C,\mathcal D,\mathcal E$ be monoidal categories, let $g$ be an oplax monoidal functor from $\mathcal C$ to $\mathcal D$ and let $G$ be a lax monoidal functor from $\mathcal D$ to $\mathc …

It is well known (e.g., Reference for "lax monoidal functors" = "monoids under Day convolution" ) that if $\mathcal C$ is a monoidal $\mathcal V$-enriched category, then a monoid in $[\mathcal C, \mat …

I'm going over what's already in the comments a little here, but: given an action of $C$ on $D$ as described, any monoid in $C$ gives rise to a monad on $D$. This is because a monoid in $C$ is just a …

We all know that A monoidal category is a bicategory with one object. How do we fill in the blank in the following sentence? A multicategory is a ... with one object. The answer is fairly …