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Unit of the monoidal category $\operatorname{Vect(k)}$

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#category-theory
43
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Is it correct to say that every locally small category C is a subcategory of the category of presheaves of that same category C?

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#category-theory
150
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Presheaf of abelian groups and presheaf kernel $\ker_{\text{pre}}\phi$.

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#algebraic-geometry #category-theory #sheaf-theory #group-homomorphism
514
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pushout as a special case of a colimit

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#general-topology #category-theory #limits-colimits
3.5k
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A monomorphism that is not injective

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#category-theory
68
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Solving an exercise on groups with universal properties

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#group-theory #category-theory
48
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Natural equivalence of endofunctors and their categories of algebras

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#category-theory #functors
83
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ETCS and existence of complements of sets

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#category-theory #set-theory #foundations
112
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Categorification of Metric Spaces

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#category-theory
138
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Is this a Fibration?

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#category-theory
404
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Galois groupoid of covering map: are endomorphisms of universal covering spaces automorphisms?

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#general-topology #algebraic-topology #category-theory #galois-theory #covering-spaces
68
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Notational question: What is $Cat(-,-)$?

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#category-theory
34
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A category is $\mathbf{J}$-complete?

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#category-theory
643
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Prove that $\emptyset$ is unique initial object in Set(proof verification).

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#proof-verification #category-theory #proof-writing
1.4k
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Why pullback in Set is defined through equality $f(a) = g(b)$

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#category-theory #pullback

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