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Since a dualizing complex has finite projective dimension if and only if R is Gorenstein, one corollary of the preceding theorem is that R is Gorenstein if and only if every
Remark 9 The category C( A ), equipped with the set of short exact sequences that have zero connectors on homology as pure short exact sequences, is an exact category with
Thus a further extensive theory arises if we can find, inside a given co-extensive algebraic category, a core variety , meaning a variety whose inclusion has a further right
A bit more 2-category theory than we have discussed here (see [Kel74]) gives us a notion of ‘lax/oplax’ framed adjunction, in which the left adjoint is oplax and the right adjoint
Motivic homology is a covariant functor on the category of schemes of finite type over k, and has the following additional properties, see [1] (the final three properties
It is proved that the above construction defines a functor from this category to the category of Lie–Leibniz algebras and in particular to Leibniz algebras; also the restriction of
Every algebraically exact category K is complete, exact, and has filtered colimits which (a) commute with finite limits and (b) distribute over products; besides (c)
For a broad collection of categories K, including all presheaf categories, the following statement is proved to be consistent: every left exact (i.e. finite-limits preserving)
