# Category: Homotopical algebra

Comodule over a Hopf algebroid
In mathematics, at the intersection of algebraic topology and algebraic geometry, there is the notion of a Hopf algebroid which encodes the information of a presheaf of groupoids whose object sheaf an
Presheaf with transfers
In algebraic geometry, a presheaf with transfers is, roughly, a presheaf that, like cohomology theory, comes with pushforwards, “transfer” maps. Precisely, it is, by definition, a contravariant additi
Homotopy associative algebra
In mathematics, an algebra such as has multiplication whose associativity is well-defined on the nose. This means for any real numbers we have . But, there are algebras which are not necessarily assoc
Derivator
In mathematics, derivators are a proposed frameworkpg 190-195 for homological algebra giving a foundation for both abelian and non-abelian homological algebra and various generalizations of it. They w
Homotopy colimit and limit
In mathematics, especially in algebraic topology, the homotopy limit and colimitpg 52 are variants of the notions of limit and colimit extended to the homotopy category . The main idea is this: if we
H-object
In mathematics, specifically homotopical algebra, an H-object is a categorical generalization of an H-space, which can be defined in any category with a product and an initial object . These are usefu
Cofibration
In mathematics, in particular homotopy theory, a continuous mapping , where and are topological spaces, is a cofibration if it lets homotopy classes of maps be extended to homotopy classes of maps whe
Cotangent complex
In mathematics, the cotangent complex is a common generalisation of the cotangent sheaf, normal bundle and virtual tangent bundle of a map of geometric spaces such as manifolds or schemes. If is a mor
Derived algebraic geometry
Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded
Homotopy Lie algebra
In mathematics, in particular abstract algebra and topology, a homotopy Lie algebra (or -algebra) is a generalisation of the concept of a differential graded Lie algebra. To be a little more specific,
Motivic cohomology
Motivic cohomology is an invariant of algebraic varieties and of more general schemes. It is a type of cohomology related to motives and includes the Chow ring of algebraic cycles as a special case. S
Homotopical algebra
In mathematics, homotopical algebra is a collection of concepts comprising the nonabelian aspects of homological algebra as well as possibly the abelian aspects as special cases. The homotopical nomen