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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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8 votes

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 Preservation of sifted colimits is in section 3.2.3 (see particularly Corollary As ...
Tyler Lawson's user avatar
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