The Parthenon in Centennial Park, in Nashville, Tennessee, is a full-scale replica of the original Parthenon in Athens. It was designed by Confederate veteran William Crawford Smith and built in 1897 as part of the Tennessee Centennial Exposition. Today the Parthenon, which functions as an art museum, stands as the centerpiece of Centennial Park, a large public park just west of downtown Nashville. Alan LeQuire's 1990 re-creation of the Athena Parthenos statue in the naos is the focus of the Parthenon just as it was in ancient Greece. Since the building is complete and its decorations were polychromed as close to the presumed original as possible, this replica of the original Parthenon in Athens serves as a monument to what is considered the pinnacle of classical architecture; the plaster replicas of the Parthenon Marbles found in the Treasury Room are direct casts of the original sculptures which adorned the pediments of the Athenian Parthenon, dating back to 438 BC. The surviving originals are housed in the British Museum in London and at the Acropolis Museum in Athens.

Nashville's nickname, the "Athens of the South", influenced the choice of the building as the centerpiece of the 1897 Centennial Exposition. A number of buildings at the exposition were based on ancient originals. However, the Parthenon was the only one, an exact reproduction, it was the only one, preserved by the city, although the Knights of Pythias Pavilion building was purchased and moved to nearby Franklin, Tennessee. Major Eugene Castner Lewis was the director of the Tennessee Centennial Exposition and it was at his suggestion that a reproduction of the Parthenon be built in Nashville to serve as the centerpiece of Tennessee's Centennial Celebration. Lewis served as the chief civil engineer for the Nashville, Chattanooga and St. Louis Railroad. Built of plaster and brick, the Parthenon was not intended to be permanent, but the cost of demolishing the structure combined with its popularity with residents and visitors alike resulted in it being left standing after the Exposition. In 1895 George Julian Zolnay was "employed to make models for the ornamentation" for the building.

Within the next 20 years, weather had caused deterioration of the landmark. Some of the most elaborate events that occurred at the Parthenon were the Spring Pageants of 1913 and 1914; these extravaganzas were theatrical productions on a massive scale. With casts of up to 500, the pageants brought in audiences from surrounding states and rail prices were lowered to encourage attendance; the entire city of Nashville reveled in the opportunity to celebrate the "Athens of the South". The 1913 performance was entitled The Fire Regained, a play written by Sidney Mttron Hirsch, featured a mythological story line enhanced by theatrical spectacle popular in that era; the 1914 production, "The Mystery at Thanatos", had a mythological plot, but was shorter and better received. A copy of the script is on file at the Nashville Public Library; the most impressive thing about these pageants was the use of visual spectacle. Both shows featured impressive displays ranging from chariot races to huge dance numbers to thousands of live birds to set pieces that shot flames, all set against the backdrop of the majestic Nashville Parthenon.

As an art museum, the Parthenon's permanent collection on the lower level is a group of 63 paintings by 19th and 20th century American artists, donated by James M. Cowan. Additional gallery spaces exhibits; the main level contains a replica, completed in 1990, of the Athena Parthenos statue, in the original Parthenon in Athens. The statue of Athena Parthenos is a reconstruction, to careful scholarly standards, of the long-lost original: she is cuirassed and helmeted, carries a shield on her left arm and a small 6-foot-high statue of Nike in her right palm, stands 42 feet high, gilt with more than 8 pounds of gold leaf. In the summertime, local theater productions use the building as a backdrop for classic Greek plays such as Euripides' Medea and Sophocles' Antigone, performing on the steps of the Parthenon. Other performances, such as Mary Zimmerman's Metamorphoses, have been done inside, at the foot of Athena's statue; the Parthenon got a full makeover in 2002 with a much needed cleaning and restoration of the exterior.

The exterior lighting was upgraded to allow the columns of the building to be illuminated with different colors than the facade, allowing a uniquely versatile display of effects for events. The Parthenon served as the location for the political rally in the climactic scene of Robert Altman's 1975 film Nashville, it was used as a backdrop for the battle against the Hydra in the 2010 film Percy Jackson & the Olympians: The Lightning Thief. It features in the title and lyrics of the song Nashville Parthenon from the album Etiquette, by Casiotone for the Painfully Alone, it was used in the 2000 PBS series Greeks: Crucible of Civilization. A poem titled "Ganymede" in Heather Ross Miller's Celestial Navigator: Writing Poems with Randall Jarrell features the Parthenon; the structure figures in the climax of the Hector Lassiter novel, Three Chords and The Truth, by Craig McDonald. Nashville Parthenon website 1909 Panoramic photograph of the Nashville Parthenon from the Library of Congress Tennessee Centennial and International Exposition Collection, 1895-1900, Tennessee State Library and Archives

In category theory, a branch of mathematics, a monad is an endofunctor, together with two natural transformations required to fulfill certain coherence conditions. Monads are used in the theory of pairs of adjoint functors, they generalize closure operators on ordered sets to arbitrary categories. A monad is a certain type of endofunctor. For example, if F and G are a pair of adjoint functors, with F left adjoint to G the composition G ∘ F is a monad. If F and G are inverse functors, the corresponding monad is the identity functor. In general, adjunctions are not equivalences—they relate categories of different natures; the monad theory matters as part of the effort to capture what it is that adjunctions'preserve'. The other half of the theory, of what can be learned from consideration of F ∘ G, is discussed under the dual theory of comonads. Throughout this article C denotes a category. A monad on C consists of an endofunctor T: C → C together with two natural transformations: η: 1 C → T and μ: T 2 → T.

These are required to fulfill the following conditions: μ ∘ T μ = μ ∘ μ T. We can rewrite these conditions using the following commutative diagrams: See the article on natural transformations for the explanation of the notations T μ and μ T, or see below the commutative diagrams not using these notions: The first axiom is akin to the associativity in monoids if we think of μ as the monoid's binary operation, the second axiom is akin to the existence of an identity element. Indeed, a monad on C can alternatively be defined as a monoid in the category E n d C whose objects are the endofunctors of C and whose morphisms are the natural transformations between them, with the monoidal structure induced by the composition of endofunctors; the power set monad is a monad on the category S e t: For a set A let T be the power set of A and for a function f: A → B let T be the function between the power sets induced by taking direct images under f. For every set A, we have a map η A: A → T; the function μ A: T → T takes a set of sets to its union.

These data describe a monad. The axioms of a monad are formally similar to the monoid axioms. In fact, monads are special cases of monoids, namely they are the monoids among endofunctors End ⁡, equipped with the multiplication given by composition of endofunctors; the categorical dual definition is a formal definition of a comonad. It is therefore a functor U {\displaystyl

Arnprior is a heritage-listed homestead and farm at Mayfield Road, Queanbeyan-Palerang Region, New South Wales, Australia. It was built from 1827 by William Ryrie, it was added to the New South Wales State Heritage Register on 18 November 1999. Arnprior has associations with the Ryrie family, dating to the 1820s. Scottish-born Stewart Ryrie immigrated to Australia in 1825 on board the Triton with his second wife Isabella Ryrie and the six children from his first marriage. Ryrie's two eldest sons were James. Stewart Ryrie had served as a deputy assistant commissary general in the British Army during the Peninsular War in 1808–1815, stationed in Spain and Portugal. On arrival to Sydney in October 1825, Ryrie took up an appointment as the deputy assistant commissary general, based at the Commissariat Stores at Circular Quay. On 22 September 1826, William and James Ryrie wrote to the Colonial Secretary Alexander Macleay, stating their intention to "reside on the Land to be granted to us" as they were unable to find suitable work in Sydney.

In c. 1827, William Ryrie was granted Portion 4 of the Parish of Larbert in the County of Murray. Ryrie's grant encompassed 2560 acres and was a rectangular parcel of land located to the north of the Shoalhaven River and to the north-east of the Village of Larbert, it appears. It appears that Bradbury held a Ticket of Occupation for the land he had been living on at Curraduck-bidgee prior to 1826.'Bradbury's Station' is shown on Robert Hoddle's 1824 map of the Braidwood District in the vicinity of Ryrie's grant. Bradbury moved to the Bungonia area. William Ryrie's land grant was named Arnprior in memory of Isabella Ryrie's family home in Scotland; the 1828 Census indicates that a house on William's 2560-acre land grant, was under construction at this time, as was a house on his brother James's grant Durran Durra. The Census recorded, it recorded that there were 35 acres of cleared land and 23 acres cultivated land at Arnprior, compared to one acre cultivated and cleared land at Durran Durra. Arnprior had 553 head of 1100 sheep, while Durran Durra had 75 cattle and 540 sheep.

The house on William's land holding faced the Shoalhaven River, but was set back from it because the river was known to flood. Physical inspection of the house suggests that it began modestly and was added to over the nineteenth century to accommodate the extended Ryrie family; the house had thirteen rooms. Stewart Ryrie retired in 1829; the following year, he arrived at Arnprior to live with his wife Isabella and their three young children: John Cassels and David, it became the family home. William's younger brothers Donald 18 years old, Stewart, aged 16 lived at Arnprior. Another resident at Arnprior in the 1830s was the Greek-born shepherd Ghikas Boulgaris, married to Mary Lyons at the property in 1836, their two youngest children and Catherine, were born at Arnprior. In 1837, William Ryrie advised the Governor of New South Wales on the best routes and staging posts for a postal service between Melbourne and Sydney. In January 1840, the Arnprior land grant was formalised; the 1841 census showed that 48 people were living at Durran Durra in that year.

The two properties had been amalgamated following the death of James Ryrie in 1840. In 1845, William Ryrie travelled to Scotland where he married his step-mother's sister Marianne Cassels. Although he returned to Australia in the interim, William died in Scotland in 1856. In 1852, Stewart Ryrie Snr died, his second youngest son Alexander managed the property until c. 1859, at which time he moved to the property he had purchased near Canberra named Micalago. Major floods hit the Braidwood and Queanbeyan districts in August 1853. Hobart newspaper The Courier reported that the "government township of Larbert was … under water, presenting the appearance of another Gundagai" and that Arnprior was "surrounded by the flood, but as it stands on higher ground than the opposite side, it escaped destruction"; the house at Arnprior "extended hospitality to the travellers on the track from Goulburn and Bungonia" through to Braidwood, who arrived late at night or were held up by floods at the adjacent ford over the Shoalhaven.

In 1853, Samuel Mossman and Thomas Bannister published their account of travelling through NSW and Victoria, at which time they visited Braidwood and Arnprior: "Further on you come to Arnprior, the estate of Mr. Ryrie in the county of Murray, on the Shoalhaven River, about 152 miles from Sydney. Here there is a considerable quantity of land enclosed, but the property is not esteemed; this road passed directly through the Ryrie property, across the ford at Larbert on the Shoalhaven River and another ford on the Boro Creek, passing through Mayfield and alongside Glen D'Or. There is some suggestion that this was a Co route. In the south-west portion of the original Arnprior grant lies a road easement leading to Lake Bathurst through Mayfield; the 1867 Postal Directory recorded that Mrs M. A. Ryrie, Helen and John Ryrie were residing at Arnprior; these were the wife and children of William Ryrie. Alexander Ryrie purchased the property from his brother John Cassels in either 1867 or 1876. By the late nineteenth cent