nLab essentially algebraic (infinity,1)-theory

Context

Higher algebra

higher algebra

universal algebra

Contents

Definition

Definition

An (finitary) essentially algebraic $\left(\infty ,1\right)$-theory is an (∞,1)-category $T$ with (finite) (∞,1)-limits.

An algebra over an essentially algebraic $\left(\infty ,1\right)$-theory in some (∞,1)-topos $𝒳$ is a (finite) $\left(\infty ,1\right)$-limit preserving (∞,1)-functor

$A:T\to 𝒳\phantom{\rule{thinmathspace}{0ex}}.$A : T \to \mathcal{X} \,.

Examples

• algebraic (∞,1)-theory, essentially algebraic $\left(\infty ,1\right)$-theory

References

Algebras over essentially algebraic $\left(\infty ,1\right)$-theories that play the role of structure sheaves of algebras are considered in

Revised on December 29, 2010 17:53:43 by Urs Schreiber (89.204.137.120)