In mathematics, The fundamental theorem of topos theory states that the slice E / X {\displaystyle \mathbf {E} /X} of a topos E {\displaystyle \mathbf...

geometry Fundamental theorem of tessarine algebra Fundamental theorem of symmetric polynomials Fundamental theorem of topos theory Fundamental theorem of ultraproducts...

étale topos, an fppf topos, or a Nisnevich topos. Another important example of a topos is from the crystalline site. In the case of the étale topos, these...

application of category theory, more specifically topos theory, has been made in mathematical music theory, see for example the book The Topos of Music, Geometric...

proposed topos theory as an alternative to traditional axiomatic set theory. Topos theory can interpret various alternatives to that theory, such as constructivism...

is a Grothendieck topos (in fact, assuming a classical metalogic, this topos will even be Boolean). We can also consider actions of monoids on sets, by...

set theory in the categorical context such as algebraic set theory; Foundations of mathematics building on categories, for instance topos theory; Abstract...

homotopy type of a topological space. In terms of category theory, the fundamental groupoid is a certain functor from the category of topological spaces...

process underlying information theory, opening with the assertion that "The fundamental problem of communication is that of reproducing at one point, either...

theorem then says that the fundamental group of X is the pushout of these two induced maps. Of course, X is the pushout of the two inclusion maps of D...

essentially of the theory of equations. For example, the fundamental theorem of algebra belongs to the theory of equations and is not, nowadays, considered as belonging...

In category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by Jonathan Mock...

category theory, a branch of mathematics, a monad (also triple, triad, standard construction and fundamental construction) is a monoid in the category of endofunctors...

topology, and representation theory. As part of this project, his creation of topos theory, a category-theoretic generalization of point-set topology, has...

American mathematician known for his work in category theory, topos theory and the philosophy of mathematics. Lawvere studied continuum mechanics as an...

types of hidden-variable theories, which try to explain the predictions of quantum mechanics in a context-independent way. The version of the theorem proved...

topology is called a site. A category of sheaves on a site is called a topos or a Grothendieck topos. The notion of a topos was later abstracted by William...

IHÉS in France, contributing to the SGA4 volumes of the Séminaire de géométrie algébrique, on topos theory and étale cohomology, jointly with Alexander Grothendieck...

Ieke (1992), Sheaves in geometry and logic: a first introduction to topos theory, Springer, ISBN 978-0-387-97710-2 Hazewinkel, Michiel; Gubareni, Nadezhda...

schemes Topos theory Langlands program Non-commutative geometry A well-known example is the Taniyama–Shimura conjecture, now the modularity theorem, which...

classifier yielded a more general kind of topos, now known as an elementary topos, and that elementary topoi were models of intuitionistic logic. In addition...

incomplete proof of the fundamental theorem of algebra. Joseph Louis Lagrange (1770) The title means "Reflections on the algebraic solutions of equations"....

Fundamental theorem of projective geometry Duality (projective geometry) Real projective plane Real projective space Segre embedding of a product of projective...

of the factors. Examples include Set and CPO, the category of complete partial orders with Scott-continuous functions. A topos is a certain type of cartesian...

version of the second fundamental theorem of calculus, that integrals can be computed using any of a function's antiderivatives. The first full proof of the...

object" is sometimes used synonymously with exponential object YX, in topos theory Y is required to be Ω. There is both a covariant and contravariant power...

homotopy of filtered spaces, higher-dimensional space structures, the construction of the fundamental groupoid of a topos E in the general theory of topoi...

the tools of operator K-theory and cyclic cohomology. Several generalizations of now-classical index theorems allow for effective extraction of numerical...

strong enough topos-, type- or constructive set theories such as C Z F {\displaystyle {\mathsf {CZF}}} , a constructive counter-part of Z F {\displaystyle...

larger theory, sharing some but not all of its axioms and theorems, and focusing on a subset of its domain. successor function A fundamental function...