symmetric monoidal (∞,1)-category of spectra
Background
Basic concepts
equivalences in/of $(\infty,1)$-categories
Universal constructions
Local presentation
Theorems
Extra stuff, structure, properties
Models
monoid theory in algebra:
The notion of monoid (or monoid object, algebra, algebra object) in a monoidal (infinity,1)-category $C$ is the (infinity,1)-categorical generalization of monoid in a monoidal category.
For $C$ a cartesian monoidal (∞,1)-category with a monoidal structure determined by the (∞,1)-functor
a monoid object of $C$ is a lax monoidal (∞,1)-functor?
This generalizes how, for monoidal categories, monoid objects are the same as lax monoidal functors
A generalization to the case that the monoidal (∞,1)-category $C$ is not Cartesian is discussed in Section 4.1.3 of Higher Algebra.
definition 1.1.14 in
An equivalent reformulation of commutative monoids in terms (∞,1)-algebraic theories is in
Last revised on August 24, 2023 at 09:19:13. See the history of this page for a list of all contributions to it.