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Presummably you could use the forgetful functor to sets and it's its adjoint to construct a homology theory (using the walking adjunction, simplicial sets, etc) analogously to how group homology arises from the forgetful-free adjunction to set.

The details are probably rather dense and tedious though.

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Presummably you could use the forgetful functor to sets and it's adjoint to construct a homology theory (using the walking adjunction, simplicial sets, etc) analogously to how group homology arises from the forgetful-free adjunction to set.

The details are probably rather dense and tedious though.