Cybersecurity and privacy risk assessment of point-of-care systems in healthcare: A use case approach

In mathematics, specifically, in category theory, a 2-functor is a morphism between 2-categories.^[1] They may be defined formally using enrichment by saying that a 2-category is exactly a Cat-enriched category and a 2-functor is a Cat-functor.^[2]

Explicitly, if C and D are 2-categories then a 2-functor $F\colon C\to D$ consists of

a function $F\colon {\text{Ob}}C\to {\text{Ob}}D$ , and
for each pair of objects $c,c'\in {\text{Ob}}C$ , a functor $F_{c,c'}\colon {\text{Hom}}_{C}(c,c')\to {\text{Hom}}_{D}(Fc,Fc')$

such that each $F_{c,c'}$ strictly preserves identity objects and they commute with horizontal composition in C and D.

See ^[3] for more details and for lax versions.

References

^ Kelly, G.M.; Street, R. (1974). Review of the elements of 2-categories. Lecture Notes in Mathematics. Vol. 420. pp. 75–103. doi:10.1007/BFb0063101. ISBN 978-3-540-06966-9. {{cite book}}: |journal= ignored (help)
^ G. M. Kelly. Basic concepts of enriched category theory. Reprints in Theory and Applications of Categories, (10), 2005.
^ 2-functor at the nLab

[1] Kelly, G.M.; Street, R. (1974). Review of the elements of 2-categories. Lecture Notes in Mathematics. Vol. 420. pp. 75–103. doi:10.1007/BFb0063101. ISBN 978-3-540-06966-9. {{cite book}}: |journal= ignored (help)

[2] G. M. Kelly. Basic concepts of enriched category theory. Reprints in Theory and Applications of Categories, (10), 2005.

[3] 2-functor at the nLab

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