Kelly Theory Of Personality Development

Gregory Maxwell 'Max' Kelly (5 June 1930 – 26 January 2007) is a mathematician who worked on category theory.

Biography[edit]

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Kelly was born in Bondi, New South Wales, Australia, on 5 June 1930.^[1] He obtained his PhD at Cambridge University in homological algebra in 1957, publishing his first paper in that area in 1959, Single-space axioms for homology theory.^[1][2] He taught in the Pure Mathematics department at Sydney University from 1957 to 1966, rising from lecturer to reader.^[1] During 1963–1965 he was a visiting fellow at Tulane University and the University of Illinois,^[1] where with Samuel Eilenberg he formalized and developed the notion of an enriched category based on intuitions then in the air about making the homsets of a category just as abstract as the objects themselves.^{[citation needed]}

He subsequently developed the notion in considerably more detail in his 1982 monograph Basic Concepts of Enriched Category Theory.^[3] Let ${\displaystyle \mathcal{V}}$ be a monoidal category, and denote by ${\displaystyle \mathcal{V}}$-Cat the category of ${\displaystyle \mathcal{V}}$-enriched categories. Among other things, Kelly showed that ${\displaystyle \mathcal{V}}$-Cat has all weighted limits and colimits even when ${\displaystyle \mathcal{V}}$ does not have all ordinary limits and colimits. He also developed the enriched counterparts of Kan extensions, density of the Yoneda embedding, and essentially algebraic theories.^{[citation needed]}

In 1967 Kelly was appointed Professor of Pure Mathematics at the University of New South Wales.^[1] In 1972 he was elected a Fellow of the Australian Academy of Science.^{[citation needed]} He returned to the University of Sydney in 1973, serving as Professor of Mathematics until his retirement in 1992.^[1] In 2001 he was awarded the Australian government's Centenary Medal. He continued to participate^[dubious] in the department as professorial fellow and professor emeritus until his death at age 76 on 26 January 2007.^[1]

Kelly worked on many other aspects of category theory besides enriched categories, both individually and in a number of collaborations.^{[citation needed]} His PhD students include Ross Street.^[2]

References[edit]

1. ^ ^abcdefgO'Connor, John J.; Robertson, Edmund F., 'Max Kelly', MacTutor History of Mathematics archive, University of St Andrews.
2. ^ ^abGregory Maxwell (Max) Kelly at the Mathematics Genealogy Project
3. ^Kelly, Gregory Maxwell (1982). Basic Concepts of Enriched Category Theory. Cambridge University Press. ISBN978-0-521-28702-9.

External links[edit]

• Max Kelly's Perpetual Web Page: a memorial page set up by Kelly's son Simon Kelly.
• 'In Memory of Max Kelly': a post at The n-Category Café, containing praise from his fellow mathematicians
• G. M. Kelly at DBLP Bibliography Server

Kelly Theory Of Attribution

In queueing theory, a discipline within the mathematical theory of probability, a Kelly network is a general multiclass queueing network.^[1] In the network each node is quasireversible and the network has a product-form stationary distribution, much like the single-class Jackson network.

The model is named after Frank Kelly who first introduced the model in 1975 in his paper Networks of Queues with Customers of Different Types.^[2]

References

1. ^Chen, H.; Yao, D. D. (2001). 'Kelly Networks'. Fundamentals of Queueing Networks. Stochastic Modelling and Applied Probability. 46. pp. 69–96. doi:10.1007/978-1-4757-5301-1_4. ISBN978-1-4419-2896-2.
2. ^Kelly, F. P. (1975). 'Networks of Queues with Customers of Different Types'(PDF). Journal of Applied Probability. 12 (3): 542–554. doi:10.2307/3212869. JSTOR3212869.