List questions from functors

Published on 23 Mar 2026 - 18:23

44

Views

Two morphisms $f, g : M \to L$ are equal as long as they are equal under the limit $L$.

Published on 22 Mar 2026 - 18:05

267

Views

Co- and contravariance of vectors vs co- and contravariant functors

Published on 20 Mar 2026 - 4:20

262

Views

Discrete simplicial sets: equivalent definitions, request for a proof

Published on 23 Mar 2026 - 1:54

145

Views

Simplicial sets, injectivity

Published on 23 Mar 2026 - 7:10

204

Views

When can functors fail to be adjoints if their hom sets are bijective?

Published on 22 Mar 2026 - 18:01

2.2k

Views

Example of a functor that doesn't reflect isomorphism

Published on 23 Mar 2026 - 8:00

653

Views

Equality of functors

Published on 22 Mar 2026 - 20:30

228

Views

Example of functor not full not faithfull

Published on 22 Mar 2026 - 18:50

97

Views

Bijective on objects implies essentially surjection

Published on 22 Mar 2026 - 21:32

2.8k

Views

Quasi-inverse of an equivalence of categories is unique up to unique isomorphism

Published on 23 Mar 2026 - 11:26

1.3k

Views

Representations and representable functors

Published on 22 Mar 2026 - 15:11

335

Views

Forgetful functor from complete metric space to metric space

Published on 17 Mar 2026 - 21:29

230

Views

Factorization of functors

Published on 22 Mar 2026 - 21:28

125

Views

Universal object of forgetful functor

Published on 22 Mar 2026 - 16:43

List Question

Continuous functor for a Grothendieck topology

Two morphisms $f, g : M \to L$ are equal as long as they are equal under the limit $L$.

Co- and contravariance of vectors vs co- and contravariant functors

Discrete simplicial sets: equivalent definitions, request for a proof

Simplicial sets, injectivity

When can functors fail to be adjoints if their hom sets are bijective?

Example of a functor that doesn't reflect isomorphism

Equality of functors

Example of functor not full not faithfull

Bijective on objects implies essentially surjection

Quasi-inverse of an equivalence of categories is unique up to unique isomorphism

Representations and representable functors

Forgetful functor from complete metric space to metric space

Factorization of functors

Universal object of forgetful functor

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