Adjoint functors: A functor can be left (or right) adjoint to another functor that maps in the opposite direction. Such a pair of adjoint functors typically arises from a construction defined by a universal property; this can be seen as a more abstract and powerful view on universal properties.
F(\mathrm{id}_{X}) = \mathrm{id}_{F(X)}\,\! for every object X \in C
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Anonymous2013-09-01 3:24
An infranatural transformation η from F to G is simply a family of morphisms ηX: F(X) → G(X). Thus a natural transformation is an infranatural transformation for which ηY ∘ F(f) = G(f) ∘ ηX for every morphism f : X → Y. The naturalizer of η, nat(η), is the largest subcategory of C containing all the objects of C on which η restricts to a natural transformation.
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Anonymous2013-09-01 10:36
Addition is commutative κ + μ = μ + κ.
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Anonymous2013-09-01 11:22
\int_{-\infty}^{\infty} \, f(t)\ dt \ = a means that the total area under f(t) is finite, and equals a