Yoneda's lemma asserts that every natural transformation between Hom functors is of this form. In other words, the Hom functors give rise to a full...

Diagonal functor : The diagonal functor is defined as the functor from D to the functor category D C which sends each object in D to the constant f...

contravariant functor is right exact if and only if it turns finite limits into colimits. A functor is exact if and only if it is both left exact a...

The distinction is particularly important for computations with tensors , which often have mixed variance (both covariant and contravariant compone...

C ) can be made precise in several ways; the most succinct formulation uses the language of adjoint functors . Every functor F  : D ? E induces a f...

Functors Main article: functor Functors are structure-preserving maps between categories. They can be thought of as morphisms in the category of al...

Left derived functors are zero on all projective objects. One may also start with a contravariant left-exact functor F ; the resulting right-derive...

Then using the rules in the definition, we find that for general vector fields and we get the first term in this formula is responsible for "twisti...

Exterior covariant derivative - Wikipedia, the free encyclopedia Exterior covariant derivative From Wikipedia, the free encyclopedia   (Redirected ...

Transformation of local covariant basis in the case of general curvilinear coordinates As stated above, contravariant vectors are vectors with cont...

In practice, for a valid statement about a particular category , the dual statement is valid in the dual category ( ). [ edit ] Duality The example...

Christoffel symbols in the y coordinate frame. Note that the Christoffel symbol does not transform as a tensor, but rather as an object in the jet ...