This article is about a concept in category theory. For the concept in cognitive psychology and philosophy, see prototype theory.
If is a category, then a -graded category is a category together with a functor
.
Monoids and groups can be thought of as categories with a single object. A monoid-graded or group-graded category is therefore one in which to each morphism is attached an element of a given monoid (resp. group), its grade. This must be compatible with composition, in the sense that compositions have the product grade.
Monoids and groups can be thought of as categories with a single object. A monoid-graded or group-gradedcategory is therefore one in which to each morphism...
homological algebra, a differential gradedcategory, often shortened to dg-category or DG category, is a category whose morphism sets are endowed with...
gradation or grading. A graded module is defined similarly (see below for the precise definition). It generalizes graded vector spaces. A graded module that...
mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra...
introduced in homological algebra, and it is widely used for graded algebras, which are graded vector spaces with additional structures. Let N {\displaystyle...
differential graded algebra is a graded associative algebra with an added chain complex structure that respects the algebra structure. A differential graded algebra...
undertaken without consent be reversed at the owner's expense. See also Category:Grade I listed buildings for more examples of such buildings across England...
may refer to the category of augmented differential graded commutative algebras. A graded Lie algebra is a Lie algebra that is graded as a vector space...
the category of modules.) Category of rings Derived category Module spectrum Category of graded vector spaces Category of abelian groups Category of representations...
This is a list of Category A listed buildings in Scotland, which are among the listed buildings of the United Kingdom. For a fuller list, see the pages...
references for details. More generally, the homotopy category Ho(C) of a differential gradedcategory C is defined to have the same objects as C, but morphisms...
psychology and cognitive linguistics, in which there is a graded degree of belonging to a conceptual category, and some members are more central than others. It...
Committee for Standardization). European standard steel grade names fall into two categories: Steel specified by purpose of use and mechanical properties...
differential gradedcategory is a category whose Hom sets are equipped with structures of differential graded modules. In particular, if the category has only...
of the winners of the Newbery Medal have been middle grade books. The category beyond middle grade is young adult, which is intended for readers between...
system used by British universities: Many courses also have Non-Graded Pass (NGP) and Non-Graded Fail (NGF), in which it is considered more appropriate to have...
highest grade and the only circuits that can host Formula One races. A circuit holding a particular grade can also host events featuring categories of cars...
teachers, funding and resources. The grades for the above subjects are normally graded as below, Candidates who receive a grade of ‘W’ are considered failed in...
equivalences are the (strong) homotopy equivalences. The category of (nonnegatively graded) chain complexes of R-modules carries at least two model structures...
categories based on their properties Primary education Educational stage Education in England Education in Scotland Are You Smarter Than a 5th Grader...
Applied category theory Category of sets Concrete categoryCategory of vector spaces Category of graded vector spaces Category of chain complexes Category of...
categories which can be associated to any point w 0 ∈ A 1 {\displaystyle w_{0}\in \mathbb {A} ^{1}} , a Z / 2 {\displaystyle \mathbb {Z} /2} -graded category...
Category 2 or Category II may refer to: Category 2 cable, a grade of unshielded twisted pair cabling Category 2 tropical cyclone, on any of the Tropical...
grade as Prime. Choice is the most common grade sold in retail outlets, and represents roughly half of all graded beef. Select is sold as a cheaper, leaner...
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