Abstract
We obtain André-Quillen homology for commutative algebras using relative homological algebra in the category of functors on finite pointed sets.
Highlights
Let Γ be the small category of finite pointed sets
All tensor products are taken over K. It was proved in [7] that π∗(L(A, M )) is isomorphic to a brave new algebra version of AndreQuillen homology HΓ∗ (A, M ) constructed by Alan Robinson and Sarah Whitehouse [10]
The main result of this paper shows that a similar isomorphism exists for Andre-Quillen homology if one takes an appropriate relative derived functor of the same functor π0 : Γ-mod → Vect
Summary
Let Γ be the small category of finite pointed sets. For any n ≥ 0, let [n] be the set {0, 1, ..., n} with basepoint 0. A left Γ-module is a covariant functor Γ → Vect to the category of vector spaces over a field K. The category Γ-mod of left Γ-modules is an abelian category with enough projective and injective objects. One can form the left derived functors of the functor π0 : Γ-mod → Vect, which we will denote by π∗. All tensor products are taken over K It was proved in [7] that π∗(L(A, M )) is isomorphic to a brave new algebra version of AndreQuillen homology HΓ∗ (A, M ) constructed by Alan Robinson and Sarah Whitehouse [10]. The main result of this paper shows that a similar isomorphism exists for Andre-Quillen homology if one takes an appropriate relative derived functor of the same functor π0 : Γ-mod → Vect
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