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4 votes
1 answer
208 views

What should be required from a model category so that the category of algebraic objects in it has the natural model structure?

I have two reference questions What should be required of a category with finite products so that a (multi-sorted, finitary) Lawvere theory induces a monadic adjunction on it? This should be ...
Arshak Aivazian's user avatar
11 votes
2 answers
755 views

When does the forgetful functor from algebras over a monad commute with homotopy geometric realizations?

Let $\mathcal{C}$ be a combinatorial model category and $\mathrm{T}$ a monad on $\mathcal{C}.$ Assume that the model structure on $\mathcal{C}$ lifts to a model structure on the category of $\...
Hadrian Heine's user avatar
4 votes
1 answer
763 views

When do reflexive coequalizers preserve weak equivalences?

In my work I've run into the following situation. In a model category, I have two reflexive coequalizers $A_i \stackrel{\to}{\to} B_i \to C_i$ and a map of diagrams which is levelwise a weak ...
David White's user avatar
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