Implication Details
Assumptions: elementary topos
Conclusions: disjoint finite coproducts, effective congruences, epi-regular, finitely cocomplete
Proof: See Mac Lane & Moerdijk, Cor. IV.5.4, Cor. IV.10.5, Thm. 4.7.8; and Johnstone, Part A, Proposition 2.4.1.
Show 27 categories using this implication
- category of algebras
- category of combinatorial species
- category of commutative algebras
- category of commutative rings
- category of filtered vector spaces
- category of finite sets
- category of finite sets and bijections
- category of Jónsson-Tarski algebras
- category of M-sets
- category of pairs of sets
- category of pointed topological spaces
- category of rings
- category of rngs
- category of set functions and commutative squares
- category of sets
- category of sets with a distinguished subset
- category of sets with finite-to-one maps
- category of sheaves
- category of simplicial sets
- category of torsion-free abelian groups
- delooping of a non-trivial finite group
- delooping of the additive monoid of ordinal numbers
- poset of natural numbers
- trivial category
- walking fork
- walking isomorphism
- walking span