Topological monoids give monoids in animae

Example 5.1.4. By Chapterexercise 5.1, a topological monoid is a monoid object in \(\Top \). Combining the preceding exercise with the fact that \(\Pi _{\infty }\colon \Top \to \An \) preserves finite products (see Corollary 2.3.20), we see that every topological monoid \(M\) defines a monoid object \(\Pi _{\infty }(M)\) in \(\An \).