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Finitely presentable objects in the categories of algebras of $\infty$-algebraic theories

No, this fails even for the infinity category of spaces, where "free" means "discrete". A coequalizer of free spaces is a wedge of circles, so for example $S^2$ is not of this form....
Tim Campion's user avatar
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Does the forgetful functor $F:\mathrm{CAlg}\to\mathrm{Alg}^{(1)}$ sending $E_\infty$-ring spectra to $E_1$-ring spectra preserve limits and colimits?

Limit-preservation is the content of section 3.2.2 of Higher Algebra (see particularly Corollary 3.2.2.5). Preservation of sifted colimits is in section 3.2.3 (see particularly Corollary 3.2.3.2). As ...
Tyler Lawson's user avatar
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