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Are two objects equivalent in a category when their hom sets are isomorphic?

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#category-theory
126
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Rotman's Homological Algebra Text, Def of Adjoint Functors

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#abstract-algebra #category-theory #homological-algebra
359
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Coproduct of abelian groups

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#category-theory #abelian-groups #direct-sum #universal-property
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Direct limit commutes with direct sums in the category of abelian groups

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#abstract-algebra #category-theory #direct-sum #limits-colimits
671
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How to understand quasi-inverse of a function f∘g∘f = f?

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#functions #category-theory #inverse #functional-equations #generalized-inverse
104
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Points of Coproducts

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#category-theory
566
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Limit of poset diagram with initial object (Vakil - exercise 1.4.A)

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#category-theory #limits-colimits
77
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Defining certain operads for general symmetric monoidal categories

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#abstract-algebra #reference-request #category-theory #operads
193
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Explicit description of a left adjoint to the forgetful functor from Unif to Top

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#general-topology #category-theory #adjoint-functors #uniform-spaces
28
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Category of representations of a tensor product algebra

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#abstract-algebra #category-theory #representation-theory
30
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Show the following arrows are transposes of each other

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#category-theory
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
127
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Proof-theoric ordinal of ETCS

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#category-theory #set-theory #ordinals #proof-theory #ordinal-analysis
63
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references for cones' homology

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#algebraic-topology #category-theory #homology-cohomology #sheaf-theory
684
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Automorphism group of a functor

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#category-theory

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