Pullback dan Pushout di Kategori Modul Topologis - Yunita Septriana Anwar; Indah Emilia Wijayanti; Budi Surodjo; Dewi Kartika Sari (Department of Matematics, Universitas Padjadjaran, 2022)
A pullback of two morphisms with a common codomain fA→ C and gB→ C is the limit of a diagram consisting f and g. The dual notion of a pullback is called a pushout. A pushout of two morphisms with a common domain kA→ B and lA→ C is the colimit of a diagram consisting k and l. The pullback and the pushout of two morphisms need not exists. In this paper, we constructed a pullback and a pushout of two morphism in category of topological modules. A pullback of two continuous homomorphisms fA→ C and gB→ C in category of topological modules is a diagram that contains A× _C B={(a,b)A× B f(a)=g(b)}A× B with the subspace topology on A× _C B. Furthermore, the pushout of two continuous homomorphisms kA→ B and lA→ C in category of topological modules is a diagram that contains B_A C=(BC)/ where is the smallest equivalence relation containing the pairs (k(a),l(a)) for all aA and topology on BC is coproduct topology τ_coprod