symmetric monoidal (∞,1)-category of spectra
An (finitary) essentially algebraic $(\infty,1)$-theory is an (∞,1)-category $T$ with (finite) (∞,1)-limits.
An algebra over an essentially algebraic $(\infty,1)$-theory in some (∞,1)-topos $\mathcal{X}$ is a (finite) $(\infty,1)$-limit preserving (∞,1)-functor
An ordinary essentially algebraic theory is a 0-truncated essentially algebraic $(\infty,1)$-theory.
If $X$ is an (∞,1)-topos, $T$-algebras in $\mathcal{X}$ correspond to left exact left adjoints $PSh(T) \to \mathcal{X}$ under the equivalence $\Fun^L(PSh(T), \mathcal{X}) \to \Fun(T, \mathcal{X})$
algebraic (∞,1)-theory, essentially algebraic $(\infty,1)$-theory
Algebras over essentially algebraic $(\infty,1)$-theories that play the role of structure sheaves of algebras are considered in
Last revised on March 12, 2024 at 17:48:59. See the history of this page for a list of all contributions to it.