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text: 'A **category** consists of a collection of objects with morphisms between them. A morphism $f$ goes from one object, say $X$, to another, say $Y$, and is drawn as an arrow from $X$ to $Y$. Note that $X$ may equal $Y$ (in which case $f$ is referred to as an [-endomorphism]). The object $X$ is called the source or [3js domain] of $f$ and $Y$ is called the target or [3lg codomain] of $f$, though note that $f$ itself need not be a [-3jy] and $X$ and $Y$ need not be sets. This is written as $f: X \\rightarrow Y$.\n\nThese morphisms must satisfy three conditions:\n\n 1. [Composition_of_functions **Composition**]: For any two morphisms $f: X \\rightarrow Y$ and $g: Y \\rightarrow Z$, there exists a morphism $X \\rightarrow Z$, written as $g \\circ f$ or simply $gf$. \n 2. [3h4 **Associativity**]: For any morphisms $f: X \\rightarrow Y$, $g: Y \\rightarrow Z$ and $h:Z \\rightarrow W$ composition is associative, i.e., $h(gf) = (hg)f$.\n 3. [identity_map **Identity**]: For any object $X$, there is a (unique) morphism, $1_X : X \\rightarrow X$ which, when composed with another morphism, leaves it unchanged. I.e., given $f:W \\rightarrow X$ and $g:X \\rightarrow Y$ it holds that: $1_X f = f$ and $g 1_X = g$.',
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