By studying categories and functors, we are not just studying a class of mathematical structures and the morphisms between them ; we are studying the relationships between various classes of mathematical structures.

By the 19th century, European cavalry fell into four main categories:

By 1951, 87 subroutines in the following categories were available for general use: floating point arithmetic ; arithmetic operations on complex numbers ; checking ; division ; exponentiation ; routines relating to functions ; differential equations ; special functions ; power series ; logarithms ; miscellaneous ; print and layout ; quadrature ; read ( input ); nth root ; trigonometric functions ; counting operations ( simulating repeat until loops, while loops and for loops ); vectors ; and matrices.

By the mid-20th century, mental health practitioners began formalizing " deviant sexuality " classifications into categories.

By the early 1970s, the skinhead subculture started to fade from popular culture, and some of the original skins dropped into new categories, such as the suedeheads ( defined by the ability to manipulate one's hair with a comb ), smoothies ( often with shoulder-length hairstyles ), and bootboys ( with mod-length hair ; associated with gangs and football hooliganism ).

By the end of the 2nd century BCE, the classification scheme had been expanded into eight categories, seen in the Art of Grammar ( Τέχνη Γραμματική ):

By votes in the commission, the commissioners are given executive responsibilities for the various county departments, which fall under the categories of " Roads and Transportation ", " Community Development ", " Environmental Services ", " Health and Human Services ", " Technlogy and Land Development ", and " Finance and General Services ".

By the end of the colonial period in 1821, over one hundred categories of possible variations of mixture existed.

According to Alberto Flores Galindo, " By the 1940 census, the last that utilized racial categories, mestizos were grouped with whites, and the two constituted more than 53 percent of the population.

By the 1620s, the Shoreditch amphitheaters had become deeply identified with the louder and less reputable categories of play-goers, such as apprentices.

By breaking down rigid categories in the mind ( according to a definition of genius put forward by Arthur Koestler ), the disease makes the thought process both faster and more flexible ; it also causes physical breakdown and, within nine months, death.

By using phenomenology, intersubjectivity and first-person categories, the humanistic approach seeks to get a glimpse of the whole person and not just the fragmented parts of the personality.

By the 1920s, a ticket purchased a varied program including a feature and several supporting works from categories such as second feature, short comedy, 5 – 10 minute cartoon, and newsreel.

By 1972 he had established or acquired a further seven businesses in these categories, including one which rented construction equipment.

By 1982 SIOP-5 contained more than 40, 000 possible targets in four categories:

By way of example one can enumerate the following categories of " data " that under coordinated antecedent plan would assume the form of variables that can be adjusted in the plan according to circumstances: rate of investment, distribution of investment between capital and consumption, choices of production techniques, geographical distribution of investment and relatives rates of growth of transport, fuel and power, and of agriculture in relation to industry, the rate of introduction of new products, and their character, and the degree of standardization or variety in production that the economy at its stage of development feels it can afford.

By using a variety of teaching methods from each of these categories, teachers offer different learning styles at once, and improve learning by challenging students to learn in different ways.

By the end of the colonial period in 1821, over one hundred categories of possible variations of mixture existed.

By constructing a potentially solipsistic world of privately-constructed virtual realities, Schroeder is able again to create ambiguities in the relationship of subject to object that undermine both categories.

By the end of the war, there were over 115, 000 refuge-seeking people of all categories in Switzerland, representing the maximum number of refugees at any one time.

By default, System Preferences organizes preference panes into several categories.

By submitting, commenting on and voting for or against stories, photos and videos that they like or don ’ t like using a democratic voting method, Mixx users can influence the flow of incoming media and recommend relevant media to other users within specific categories like business, sports and health using either free-form or pre-determined meta tags to define items by subject matter or geography.

By the late 1960s, the Soviet Union had reached a rough parity with the United States in some categories of strategic weaponry, and at that time offered to negotiate limits on strategic nuclear weapons deployments.

By far the most important two categories of federal subject-matter jurisdiction in non-criminal cases are federal question jurisdiction and diversity jurisdiction.

By the 1970s, scientists such as John Money had come to see gender identity as socially constructed rather than rooted in genetics.

By 1980, most feminist writings had agreed on using gender only for socioculturally adapted traits.

By the Interpretation Act of 2005, no incumbent appointee of the Crown is affected by the death of the monarch, nor are they required to take the Oath of Allegiance again, and all references in legislation to previous monarchs, whether in the masculine ( e. g. His Majesty ) or feminine ( e. g. the Queen ), continue to mean the reigning sovereign of Canada, regardless of his or her gender.

# By coming out, trans and intersex people disclose their gender identity and, if applicable, their decision to transition to the gender role with which they more closely identify.

By gender, 48. 6 % are men and 51. 4 % are women.

By doing this, they fail to notice the difference between the third genders as primarily being of feminine gender, and tend to put this difference down to the gender role of the third genders, of being anally or orally penetrated.

By gender the canton is nearly evenly split with 50. 9 % male and 49. 1 % female.

By relying on identity information, such as that publicly traceable to telephone numbers or voter registration addresses and that voluntarily provided by respondents such as age and gender, polls can be made more scientific.

By the early 1980s, it was largely perceived that women had met their goals and succeeded in changing social attitudes towards gender roles, repealing oppressive laws that were based on sex, integrating the " boys ' clubs " such as Military academies, the United States armed forces, NASA, single-sex colleges, men's clubs, and the Supreme Court, and illegalizing gender discrimination.

By gender: Available studies consistently indicate that in every region of the world, and at all ages, females have a significantly higher risk of being visually impaired than males.

By imagining a new gender and resultant sexual orientation, the story allows readers to reflect on the real world while maintaining an estranging distance.

By besting the Thing in combat, she feels she can prove once and for all that women were superior to the male gender, and finally end a stagnant war between Femizonia and the warlike, male dominated planet of Machus, where the female population had been subjugated by its ruler Mahkizmo.

By the time of his mid or late-adult years, Ryan developed a sick insatiable taste for the female gender, and he began attacking prostitutes and stray women with the cunning of a wild animal.

; By gender

By redeploying those practices of identity and exposing as always failed the attempts to " become " one's gender, Butler believes that a positive, transformative politics can emerge.

By focusing on such groups, historians have, " inspired new debates over the roles of class, gender, and race in accounting for human divisions and inequalities.

By showing clearly the economic contributions that midwives made to their households and local communities, and demonstrating the organizational skill of multitasking as a source of female empowerment, the book revises the understanding of prescribed gender roles.

By portraying African-American women as self-defined, self-reliant individuals confronting race, gender, and class oppression, Afrocentric feminist thought speaks to the importance that knowledge plays in empowering oppressed people. One distinguishing feature of Black feminist thought is its insistence that both the changed consciousness of individuals and the social transformation of political and economic institutions constitute essential ingredients for social change.

By tracing the nature and extent of their participation in intellectual and political debates, it was possible to show the degree to which women's actions diverged not only from conservative gender models but also from their own formulations concerning women's proper social role.