Oplysninger om | engelsk ord SUBOBJECT

Eksempler på brug af SUBOBJECT i en sætning

• Cokernels are dual to the kernels of category theory, hence the name: the kernel is a subobject of the domain (it maps to the domain), while the cokernel is a quotient object of the codomain (it maps from the codomain).
• It proposes simple quantum models of space-time based on category-theoretic notions of a topos and its subobject classifier (which has a Heyting algebra structure, but not necessarily a Boolean algebra structure).
• In category theory, a subobject classifier is a special object Ω of a category such that, intuitively, the subobjects of any object X in the category correspond to the morphisms from X to Ω.
• Since the detailed structure of objects is immaterial in category theory, the definition of subobject relies on a morphism that describes how one object sits inside another, rather than relying on the use of elements.
• This result of Grothendieck follows from the existence of a generator of the category (it can be written down explicitly, and is related to the subobject classifier).
• This map is in fact a monomorphism in the category σ-Hom, and therefore H is a subobject of G which is not an induced substructure.
• rightAs noted above, a topos C has a subobject classifier Ω, namely an object of C with an element t ∈ Ω, the generic subobject of C, having the property that every monic m: X′ → X arises as a pullback of the generic subobject along a unique morphism f: X → Ω, as per Figure 1.

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