internalization and categorical algebra
algebra object (associative, Lie, …)
symmetric monoidal (∞,1)-category of spectra
A Lawvere theory is encoded in its syntactic category , a category with finite products such that all objects are finite products of a given object.
An algebra over a Lawvere theory , or -algebra for short, is a model for this algebraic theory: it is a product-preserving functor
The category of -algebras is the full subcategory of the functor category on the product-preserving functors
For more discussion, properties and examples see for the moment Lawvere theory.
The category has all limits and these are computed objectwise, hence the embedding preserves these limits.
is a reflective subcategory of :
With the above this follows using the adjoint functor theorem.
The category has all colimits.
for more see Lawvere theory for the moment
Last revised on March 22, 2021 at 09:18:46. See the history of this page for a list of all contributions to it.