Dinatural transformation

{{Short description|Generalization of natural transformations}}In category theory, a branch of mathematics, a dinatural transformation $\alpha$ between two functors

: $S,T : C^{\mathrm{op}}\times C\to D,$

written

: $\alpha : S\ddot\to T,$

is a function that to every object $c$ of $C$ associates an arrow

: $\alpha_c : S(c,c)\to T(c,c)$ of $D$

and satisfies the following coherence property: for every morphism $f:c\to c'$ of $C$ the diagram

center

commutes.{{cite book|url={{Google books|gfI-BAAAQBAJ|page=218|plainurl=yes}} |last1=Mac Lane |first1=Saunders |author-link = Saunders Mac Lane|title=Categories for the working mathematician |date=2013 |publisher=Springer Science & Business Media |page=218}}

The composition of two dinatural transformations need not be dinatural.

Notes

References

{{citation

|url={{Google books|cfIuEAAAQBAJ&dq|page=23|plainurl=yes}}

| isbn=9781108746120

| date=22 July 2021

| publisher=Cambridge University Press

| first1=Loregian|last1=Fosco| title=(Co)end Calculus

| doi=10.1017/9781108778657

arxiv=1501.02503 | s2cid=237839003

}}

{{cite book |url={{Google books|vTF7CwAAQBAJ|page=126|plainurl=yes}} |doi=10.1007/BFb0060443 |chapter=Dinatural transformations |title=Reports of the Midwest Category Seminar IV |series=Lecture Notes in Mathematics |date=1970 |last1=Dubuc |first1=Eduardo |last2=Street |first2=Ross |volume=137 |pages=126–137 |isbn=978-3-540-04926-5 }}

External links

{{nlab|id=dinatural+transformation|title=dinatural transformation}}

Category:Functors

Dinatural transformation

See also

Notes

References

External links