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We also show an additive functor preserves the homology of all differential objects if and only if it is exact and find necessary and sufficient conditions on a differential object
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
As we shall see below, any countable strongly connected category with a terminal object can be fully embedded into Alg(1 × 2) by a functor preserving limits over finitely many
Abstract. In this article we expose a proof of the Canonical Decomposi- tion Theorem of irreducible 3-manifolds along tori and annuli, also known as JSJ Theorem. This proof will
Since the saturation of an A-subsheaf of E is an A-subsheaf of E , the usual proof of the existence of an Harder - Narasimhan filtration of any vector bundle on X (see for instance
On the basis of this theorem, necessary and sufficient conditions are obtained for a weak homomorphism (resp. its adjoint operator, resp. its double adjoint operator) to be again
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
Let O be a set and V be a locally presentable cofibrantly generated monoidal simplicial model category with a monoidal fibrant replacement functor.. Then the category of V O
