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

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...

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

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...

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...

It follows that any functor which preserves limits will take terminal objects to terminal objects, and any functor which preserves colimits will ta...

Categorical logic originated with Bill Lawvere 's Functorial Semantics of Algebraic Theories (1963), and Elementary Theory of the Category of Sets ...

X i , f ij ) be a direct system of objects and morphisms in a category C (same definition as above). The direct limit of this system is an object X...

B , the pullback X × B E is a fiber bundle over X called the pullback bundle . The associated commutative diagram is a morphism of fiber bundles. I...

Practical geometry 2.2 Axiomatic geometry 2.3 Geometric constructions 2.4 Numbers in geometry 2.5 Geometry of position 2.6 Geometry beyond Euclid 2...

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

Contents 1 Moduli of curves 2 Moduli of varieties 3 Moduli of vector bundles 4 Constructions 5 Fine versus coarse moduli spaces 5.1 Why do most mod...