G -sets are nothing but functors from this category to Set The category of all directed graphs is cartesian closed; this is a functor category as e...

Problems formulated with adjoint functors 1.3 Adjoint functors as solving optimization problems 1.4 The case of partial orders 2 Formal definitions...

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...

Beck's monadicity theorem gives a characterization of monadic functors. [ edit ] Uses Monads are used in functional programming to express types of...

Indeed, the term "zero object" originated in the study of preadditive categories like Ab , where the zero object is the zero group . A preadditive ...

Another article treats the concept of species in biology . In combinatorial mathematics , the theory of combinatorial species is an abstract, syste...

Universal cones Limits and colimits are defined as universal cones . That is, cones through which all other cones factor. A cone ? from L to F is a...

Intrinsic y = r ( s ) s = t Parametric Cartesian x = x ( t ) y = y ( t ) Involute Parametric Cartesian x = x ( t ) y = y ( t ) Pedal curve with ped...

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

Given again the finite-dimensional case, if bases have been chosen, then the composition of linear maps corresponds to the matrix multiplication , ...

Representation of affine transformations 2 Properties of affine transformations 3 Affine transformations and linear transformations 4 Affine transf...