CatDat/databases/catdat/data/categories/2.yaml at d348a8bfdfede2a29dd7f1e34d39bc1eb5b72723 · ScriptRaccoon/CatDat · GitHub

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id: '2'
name: discrete category on two objects
notation: $\2$
objects: two objects $0$ and $1$
morphisms: only the two identity morphisms
description: A concrete representation is the full subcategory of <a href="/category/CRing">$\CRing$</a> consisting of the two fields $\IF_2$ and $\IF_3$.
nlab_link: null

tags:
  - finite
  - thin

related:
  - '1'

satisfied_properties:
  - property: discrete
    proof: This is trivial.

  - property: finite
    proof: This is trivial.

  - property: small
    proof: This is trivial.

  - property: inhabited
    proof: This is trivial.

unsatisfied_properties:
  - property: connected
    proof: The objects $0$, $1$ have no zig-zag path between them.

special_objects: {}

special_morphisms:
  isomorphisms:
    description: every morphism
    proof: This is trivial.
  monomorphisms:
    description: every morphism
    proof: This is trivial.
  epimorphisms:
    description: every morphism
    proof: This is clear since it is discrete.
  regular monomorphisms:
    description: same as monomorphisms
    proof: This is because the category is mono-regular.
  regular epimorphisms:
    description: same as epimorphisms
    proof: This is because the category is epi-regular.