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$C_n(X;G)$ is naturally isomorphic to $C_n(X) \otimes G$

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#algebraic-topology #category-theory #homology-cohomology #homological-algebra #natural-transformations
140
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Question concerning the existence of natural transformations of two conjugate functors of groups regarded as categories.

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#proof-writing #category-theory #natural-transformations
149
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Can the left/right-inverse of natural transformation be analogous to the left/right inverse of a function between hom-set?

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#reference-request #category-theory #inverse #functors #natural-transformations
225
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Self-Natural Maps for Forgetful Functor

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#category-theory #functors #natural-transformations #forgetful-functors
159
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Natural transformation between $\mathcal{F}$ and $\mathcal{G}$

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#category-theory #natural-transformations
632
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Various examples of non-representable functors

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#category-theory #examples-counterexamples #natural-transformations
79
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Kunneth formula proof doubt, and natural transformation

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#homology-cohomology #homological-algebra #natural-transformations
83
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Categorical interpretation of modules (over algebras)

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#category-theory #modules #natural-transformations
457
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The inverse of a natural isomorphism is a natural isomorphism

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#category-theory #natural-transformations
59
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Natural isomorphism in linearly distributive categories with left and right dualities

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#category-theory #monoidal-categories #natural-transformations
89
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Generalized diagrams

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#category-theory #terminology #natural-transformations
181
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Monoidal adjunction whose right-adjoint functor has structure morphisms which are epimorphisms

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#category-theory #tensor-products #natural-transformations #epimorphisms
265
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"Natural" equivalence of categories?

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#reference-request #category-theory #functors #natural-transformations
170
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A question about adjoint functors:

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#category-theory #adjoint-functors #natural-transformations #kan-extensions
52
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Does isomorphism of sets of natural transformations imply isomorphism between functors?

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#category-theory #functors #natural-transformations

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