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Solving Problems Categorically

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Universal property
Adjoint functors
Monad (category theory)
Representable functor
Examples
Free object
Direct product
Direct sum
Free group
Free lattice
Grothendieck group
Dedekind–MacNeille completion
Product topology
Stone–Čech compactification
Tensor product
Inverse limit
Direct limit
Kernel (category theory)
Cokernel
Pullback (category theory)
Pushout (category theory)
Equaliser (mathematics)
Group ring