algebra over a Lawvere theory
Algebras and modules
Model category presentations
Geometry on formal duals of algebras
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 :
The category has all colimits.
for more see Lawvere theory for the moment
Revised on February 12, 2014 07:50:50
by Urs Schreiber