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**1 - 2**of**2**### ON HOMOTOPY VARIETIES

, 2005

"... Abstract. Given an algebraic theory T, a homotopy T-algebra is a simplicial set where all equations from T hold up to homotopy. All homotopy T-algebras form a homotopy variety. We will give a characterization of homotopy varieties analogous to the characterization of varieties. We will also study ho ..."

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Abstract. Given an algebraic theory T, a homotopy T-algebra is a simplicial set where all equations from T hold up to homotopy. All homotopy T-algebras form a homotopy variety. We will give a characterization of homotopy varieties analogous to the characterization of varieties. We will also study homotopy models of limit theories which leads to homotopy locally presentable categories. These were recently considered by Simpson, Lurie, Toën and Vezzosi. 1.

### Accessible categories and . . .

, 2007

"... Accessible categories have recently turned out to be useful in homotopy theory. This text is prepared as notes for a series of lectures at ..."

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Accessible categories have recently turned out to be useful in homotopy theory. This text is prepared as notes for a series of lectures at