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Adjoints are Kan extensions

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#category-theory #adjoint-functors #kan-extensions
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A question about adjoint functors:

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#category-theory #adjoint-functors #natural-transformations #kan-extensions
222
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How to understand the effect of adjoint functors?

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#category-theory #limits-colimits #adjoint-functors #universal-property #kan-extensions
399
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Kan extension and representable functors

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#category-theory #sheaf-theory #simplicial-stuff #kan-extensions
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Comma categories and Kan Extensions

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#reference-request #category-theory #kan-extensions
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Kan extension as a limit: an example

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#category-theory #limits-colimits #kan-extensions
77
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Usage of Yoneda lemma to show ${\rm Lan}_K \dashv \mathcal{E}^K$

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#category-theory #adjoint-functors #yoneda-lemma #kan-extensions
49
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Isomorphism of Left Kan extensions

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#category-theory #kan-extensions
94
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On the two definitions of derived functor in general triangulated category.

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#category-theory #homological-algebra #derived-functors #triangulated-categories #kan-extensions
128
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Example of Day convolution

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#abstract-algebra #category-theory #representation-theory #bimodules #kan-extensions
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Kan extension of a composition

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#category-theory #kan-extensions
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Toy examples for Kan extensions

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#reference-request #category-theory #big-list #kan-extensions
95
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When is an isomorphism between representable functors natural?

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#category-theory #yoneda-lemma #kan-extensions
94
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Kan extension and singular cohomology

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#algebraic-topology #homology-cohomology #model-categories #kan-extensions
160
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Are extensions of simplicial objects to functors $\mathsf{sSet} \to \mathsf{C}$ Kan extensions?

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#category-theory #simplicial-stuff #yoneda-lemma #kan-extensions

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