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In mathematics, an adjunction space (or attaching space) is a common construction in topology where one topological space is attached or "glued" onto another...

Adjoint functors in category theory Adjunction (field theory) Adjunction formula (algebraic geometry) Adjunction space in topology Conjugate transpose of...

{\mathcal {D}}} , and indeed every equivalence is an adjunction. In many situations, an adjunction can be "upgraded" to an equivalence, by a suitable natural...

map we can "glue" Y to another space X along Z using an "attaching map" f : Z → X. The result is the adjunction space X ∪ f Y {\displaystyle X\cup _{f}Y}...

limits with the final topology and initial topology respectively. Adjunction spaces are an example of pushouts in Top. The monomorphisms in Top are the...

the sphere S 2 . {\displaystyle S^{2}.} Adjunction space. More generally, suppose X {\displaystyle X} is a space and A {\displaystyle A} is a subspace of...

especially in algebraic geometry and the theory of complex manifolds, the adjunction formula relates the canonical bundle of a variety and a hypersurface inside...

mentioned above, any adjunction gives rise to a monad. Conversely, every monad arises from some adjunction, namely the free–forgetful adjunction T ( − ) : C ⇄...

The United States Space Force (USSF) is the space service branch of the United States Armed Forces. Along with the Air Force, it is part of the Department...

and is an example of Eckmann–Hilton duality. This adjunction is a special case of the adjunction explained in the article on smash products. The reduced...

right adjoint to the reduced suspension. This adjunction accounts for much of the importance of loop spaces in stable homotopy theory. (A related phenomenon...

Wedge sum Smash product Adjunction space Cohomotopy Cohomotopy group Brown's representability theorem Eilenberg–MacLane space Fibre bundle Möbius strip...

In mathematics, the tensor-hom adjunction is that the tensor product − ⊗ X {\displaystyle -\otimes X} and hom-functor Hom ⁡ ( X , − ) {\displaystyle \operatorname...

Pointed space Wedge sum Smash product Cone (topology) Adjunction space Topological algebra Topological group Topological ring Topological vector space Topological...

Tychonoff plank Vague topology Warsaw circle List of natural topologies. Adjunction space Disjoint union (topology) Extension topology Initial topology Final...

starship Voyager. Her full Borg designation was Seven of Nine, Tertiary Adjunct of Unimatrix Zero One. While her birth name became known to her crewmates...

the category of presheaves, and i {\displaystyle i} is the unit of the adjunction. In this way, the category of sheaves turns into a Giraud subcategory...

The European Space Agency (ESA) is a 22-member intergovernmental body devoted to space exploration. With its headquarters in Paris and a staff of around...

verify that for every space X, Ω(X) is spatial and for every locale L, pt(L) is sober. Hence, it follows that the above adjunction of Top and Loc restricts...

two extremal solutions to the question: "Does every monad arise from an adjunction?" The other extremal solution is the Eilenberg–Moore category. Kleisli...