category of elements in nLab
The category of elements of a functor F : C → F : \mathcal{C} \to Set is a category el ( F ) → C el(F) \to \mathcal{C} sitting over the domain ...
A category is a combinatorial model for a directed space – a “directed homotopy 1-type” in some sense. It has “points”, called objects, and also ...
Category of elements - Wikipedia
In category theory, a branch of mathematics, the category of elements of a presheaf is a category associated to that presheaf whose objects are the elements ...
An element of a set is a thing which “belongs to,” or “is an element of,” that set. The circularity of this definition is unavoidable in foundational set ...
category of generalized elements in nLab
Definition · objects are such generalized elements δ : pt D → d \delta : pt_D \to d of objects d ∈ D d \in D ; · morphisms δ → γ \delta \to \ ...
Elements of ∞-Category Theory in nLab
This pages compiles material related to the book Emily Riehl and Dominic Verity. Elements of ∞-category theory Cambridge Studies in Advanced Mathematics
Morphisms in the category of elements - MathOverflow
There are two constructions: the covariant category of elements of a copresheaf C→Set and the contravariant category of elements of a presheaf C ...
nLab element in an abelian category
Not every abelian category is a concrete category, such as Ab or R R Mod, hence its objects do not necessarily have underlying sets whose ...
generalized elements in monoidal categories - MathOverflow
In a category C, a generalized element of an object A means a morphism to A. It follows from Yoneda lemma that the object A is determined by the ...
Category theory vs. set theory ; elements, objects ; -, morphisms ; functions, functors ; equations between elements, isomorphisms between objects.
nLab - More General Discussion | The n-Category Café
where V V is our enriching category (Set or SimpSet, notably) which we are to think of as the functor which describes a generalized space X X by ...
Idea Of Ends On nLab - category theory - Math Stack Exchange
First, every group G can be considered as a special kind of category. This category, often notated BG consists of a single object ...
Everything about Category Theory : r/math - Reddit
Now how do you define "elements" of sets, when sets are themselves just objects of some category? ... nLab pages: Yoneda reduction, co-Yoneda ...
3000 and One Things to Think About | The n-Category Café
nLab - Latest Changes — Sep 17, 2009; Inbound Citations — Sep 15 ... elements of G G are distances which specify how closely related two ...
In Set Set · In concrete categories · Global elements · In toposes · In monoidal categories · For generators · In presheaf categories · In abelian ...
Defining a monoidal category without elements - Math Stack Exchange
Defining a monoidal category without elements ; an object M · | ; a 1-morphism μ · M ; a 1-morphism η · I ; a 2-isomorphism αM · μ ; a 2-isomorphism λM ...
In an enriched category, the set of morphisms (the hom-set) associated with every pair of objects is replaced by an object in some fixed monoidal category of " ...
The homunculus brain and categorical logic
fied, i.e. the elements a ∈ A are all taken to the value ... Available at: https://ncatlab.org/ · nlab/show/syntactic+category [visited on 3 November 2020].
category of presheaves in nLab
Contents · 1. Definition · 2. Properties. General; (Co-)Monadicity over Families; Functoriality; Characterization; Presheaves on over-categories and over- ...
The nLab - the (n-)category as a "grand narrative" in mathematics ...
A category is simply a collection of objects and morphisms. In some categories, morphisms represent functions, but in others, they do not.