My question is the following: is there an analog of Morita theorem in the simplicial setting? I mean, we can define two simplicial rings $A,B$ to be simplicially Morita equivalent is the categories ...
Let $R$ be a commutative unital ring and $A$ an associative (unital) $R$-algebra. What is an augmented $R$-algebra? A (unital) $R$-algebra $A$, together with a (unital) ring morphism $\varepsilon: ...
The forgetful functor from the category of rings to the category of sets does not preserve arbitrary colimits. But it does preserve filtered colimits. For example, the colimit of a sequence of rings ...