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A triple in CAT

Published online by Cambridge University Press:  20 January 2009

Charles Wells
Charles Wells
Affiliation:
Department of Mathematics and StatisticsCase Western Reserve UniversityUniversity CircleCleveland, Ohio, 44106, U.S.A.
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A triple (or monad) in a category K is a triple = (T, μ, η) where, T: K → K is a functor and μ: TT →, T, η: 1k → T are natural transformations for which (1.1) and (1.2) commute:

In these diagrams the component of a natural transformation α at an object x is denoted xα. Thus for example (kη)T is the value of the functor T applied to the component of η at k, whereas (kT)η is the component of η at the object kT. I write functions and functors on the right and composition from left to right.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 23 , Issue 3 , October 1980 , pp. 261 - 268
Copyright
Copyright © Edinburgh Mathematical Society 1980

References

REFERENCES

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