Implication Details
Claim: If a category is an elementary topos, then it has disjoint finite coproducts and has effective congruences and is epi-regular and is 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 29 categories using this implication
- trivial category
- category of algebras
- category of finite sets and bijections
- delooping of the additive monoid of ordinal numbers
- category of commutative algebras
- category of commutative rings
- category of filtered vector spaces
- category of finite sets
- category of Jónsson-Tarski algebras
- category of M-sets
- category of sets with a distinguished subset
- partially ordered set of natural numbers
- category of rings
- category of rngs
- category of sets
- category of set functions and commutative squares
- category of sets with finite-to-one maps
- category of pairs of sets
- category of sheaves
- category of combinatorial species
- category of pointed topological spaces
- category of torsion-free abelian groups
- real interval [0,1]
- category of simplicial sets
- walking commutative square
- walking composable pair
- walking fork
- walking isomorphism
- walking span