fundamentals are crucial building blocks for understanding more complex concepts in Topos Theory. This section introduces key morphisms like monomorphisms, epimorphisms, and isomorphisms, which generalize familiar concepts from set theory to broader categorical settings.
Functors, the focus of the next part, are essential tools for connecting different categories. They allow us to map objects and morphisms between categories while preserving important structural relationships, forming the basis for more advanced categorical constructions.
Category Theory Fundamentals
Monomorphisms, epimorphisms, and isomorphisms
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f:A→B in category C acts like injective function generalizes injectivity from Set theory
Left-cancellative property ensures for morphisms g,h:X→A, f∘g=f∘h implies g=h
Examples: inclusion maps (subsets), group homomorphisms with trivial kernel
Morphism f:A→B in category C behaves like surjective function extends surjectivity concept
Right-cancellative property guarantees for morphisms g,h:B→Y, g∘f=h∘f implies g=h