A **simplicially enriched category** is an extension of the concept of a category that incorporates hom-sets enriched over simplicial sets instead of sets. To unpack this, let's recall a few concepts: 1. **Category**: A category consists of objects and morphisms (arrows) between those objects, satisfying certain composition and identity axioms. 2. **Enrichment**: A category is said to be enriched over a certain structure (like sets, groups, etc.
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