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Universal algebra is the field of mathematics that studies algebraic structures themselves, not examples ("models") of algebraic structures. For instance, rather than take particular groups as the object of study, in universal algebra one takes the class of groups as an object of study.
In mathematical logic, New Foundations (NF) is an axiomatic set theory, conceived by Willard Van Orman Quine as a simplification of the theory of types of Principia Mathematica. Quine first proposed NF in a 1937 article titled "New Foundations for Mathematical Logic"; hence the name. Much of this entry discusses NF with urelements (NFU), an important variant of NF due to Jensen and clarified by Holmes. In 1940 and in a revision in 1951, Quine introduced an extension of NF sometimes called "Mathematical Logic" or "ML", that included proper classes as well as sets.
In mathematics, a multicategory is a generalization of the concept of category that allows morphisms of multiple arity. If morphisms in a category are viewed as analogous to functions, then morphisms in a multicategory are analogous to functions of several variables. Multicategories are also sometimes called operads, or colored operads.
In mathematics, an operad is a structure that consists of abstract operations, each one having a fixed finite number of inputs (arguments) and one output, as well as a specification of how to compose these operations. Given an operad , one defines an algebra over to be a set together with concrete operations on this set which behave just like the abstract operations of . For instance, there is a Lie operad such that the algebras over are precisely the Lie algebras; in a sense abstractly encodes the operations that are common to all Lie algebras. An operad is to its algebras as a group is to its group representations.
In geometry, the octahemioctahedron or allelotetratetrahedron is a nonconvex uniform polyhedron, indexed as U3. It has 12 faces (8 triangles and 4 hexagons), 24 edges and 12 vertices. Its vertex figure is a crossed quadrilateral.
In mathematics, higher category theory is the part of category theory at a higher order, which means that some equalities are replaced by explicit arrows in order to be able to explicitly study the structure behind those equalities. Higher category theory is often applied in algebraic topology, where one studies algebraic invariants of spaces, such as their fundamental weak ∞-groupoid.
In category theory, a weak n-category is a generalization of the notion of strict n-category where composition and identities are not strictly associative and unital, but only associative and unital up to coherent equivalence. This generalisation only becomes noticeable at dimensions two and above where weak 2-, 3- and 4-categories are typically referred to as bicategories, tricategories, and tetracategories. The subject of weak n-categories is an area of ongoing research.
In the theory of operads in algebra and algebraic topology, an A∞-operad is a parameter space for a multiplication map that is homotopy coherently associative.
In the theory of operads in algebra and algebraic topology, an E∞-operad is a parameter space for a multiplication map that is associative and commutative "up to all higher homotopies".
This is a timeline of category theory and related mathematics. Its scope is taken as:
Infinity is something which is boundless, endless, or larger than any natural number. It is often denoted by the infinity symbol .
In mathematics, a highly structured ring spectrum or -ring is an object in homotopy theory encoding a refinement of a multiplicative structure on a cohomology theory. A commutative version of an -ring is called an -ring. While originally motivated by questions of geometric topology and bundle theory, they are today most often used in stable homotopy theory.
In mathematics, more specifically category theory, a quasi-category is a generalization of the notion of a category. The study of such generalizations is known as higher category theory.
In mathematics, an -algebra in a symmetric monoidal infinity category C consists of the following data:
Avengers: Infinity War is a 2018 American superhero film based on the Marvel Comics superhero team the Avengers. Produced by Marvel Studios and distributed by Walt Disney Studios Motion Pictures, it is the sequel to The Avengers (2012) and Avengers: Age of Ultron (2015), and the 19th film in the Marvel Cinematic Universe (MCU). Directed by Anthony and Joe Russo and written by Christopher Markus and Stephen McFeely, the film features an ensemble cast including Robert Downey Jr., Chris Hemsworth, Mark Ruffalo, Chris Evans, Scarlett Johansson, Benedict Cumberbatch, Don Cheadle, Tom Holland, Chadwick Boseman, Paul Bettany, Elizabeth Olsen, Anthony Mackie, Sebastian Stan, Danai Gurira, Letitia Wright, Dave Bautista, Zoe Saldaña, Josh Brolin, and Chris Pratt. In the film, the Avengers and the Guardians of the Galaxy attempt to prevent Thanos from collecting the six all-powerful Infinity Stones as part of his quest to kill half of all life in the universe.
Colors Infinity is an Indian pay television channel owned by Viacom18. It primarily airs popular shows from the United States and the United Kingdom along with a few original shows to appeal to the English-speaking population of India and a few other South Asian countries. The channel was co-curated by Karan Johar and Alia Bhatt.
The Samsung Galaxy A series is a line of mid-range smartphones and tablets manufactured by Samsung Electronics as part of their Galaxy line. The first model in the series was the first-generation Galaxy Alpha, released on 31 October 2014.
In category theory, a branch of mathematics, an opetope, a portmanteau of "operation" and "polytope", is a shape that captures higher-dimensional substitutions. It was introduced by John C. Baez and James Dolan so that they could define a weak n-category as a certain presheaf on the category of opetopes.
E∞ or E-infinity may refer to:
In mathematics, an algebra such as has multiplication whose associativity is well-defined on the nose. This means for any real numbers we have
References
- Heuts, Gijs; Hinich, Vladimir; Moerdijk, Ieke (2016). "On the equivalence between Lurie's model and the dendroidal model for infinity-operads". Advances in Mathematics . 302: 869–1043. arXiv: 1305.3658 . doi: 10.1016/j.aim.2016.07.021 . S2CID 119254588.
